Best Known (108, ∞, s)-Nets in Base 27
(108, ∞, 324)-Net over F27 — Constructive and digital
Digital (108, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (108, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
(108, ∞, 325)-Net over F27 — Digital
Digital (108, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (108, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
(108, ∞, 2871)-Net in Base 27 — Upper bound on s
There is no (108, m, 2872)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (108, 5741, 2872)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275741, 2872, S27, 2, 5633), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 976269 530082 831311 069575 892177 360042 089013 361531 360232 692659 986014 035063 450681 935380 900693 705942 616180 993177 621127 229558 345925 056977 962432 908900 064704 524907 455199 792312 853662 050651 874237 466997 182354 048755 979403 235659 381442 535248 005408 235498 788526 659989 199399 980271 755147 732957 689909 612535 737330 560460 468739 559365 926365 296354 462683 393023 453616 126001 717824 977394 543986 826776 350815 422397 998716 305284 655689 834993 373611 797801 383017 422432 226677 506028 188845 594762 628371 752922 628365 626934 035783 666426 394141 126805 846676 053572 619504 814196 368370 742283 875281 578208 360914 097033 489354 735485 626970 894515 609263 079760 433143 781015 153499 969186 111644 110078 999578 845723 716925 230108 098295 623473 072521 989589 455144 187064 611495 180073 838943 790261 929025 094068 228958 059531 496000 572272 875487 759174 541651 907891 715476 313431 003462 950229 622761 088409 623833 716587 870741 904225 576877 880124 649300 217554 341515 423920 513051 772572 800368 619402 408058 472636 825634 464949 618458 004793 805066 254884 890018 584100 504891 966928 435372 877926 120940 944195 687764 095961 728127 137403 733587 519152 466336 231015 143184 920803 073508 696671 883217 091950 097091 708366 574083 435491 220767 919660 114491 940230 551248 806124 717235 725697 276826 591831 457249 243477 141377 506398 785398 178879 247179 172625 874911 138508 963062 820464 611046 531536 411402 188814 040277 170211 876227 171274 342718 944680 416080 518928 546499 454815 137035 817532 856159 453290 987096 894020 459118 084969 982769 743955 489600 544817 973666 105904 936238 987401 175495 509668 958391 685693 639521 575253 046697 417445 204124 943807 916397 928760 074682 465622 061511 575996 634353 731318 349001 080521 507254 460522 745353 130175 059951 307053 237328 165638 457177 985291 197358 424730 105722 617559 332935 292033 740826 943161 670609 523535 811748 216719 218072 931917 523370 545748 977835 616235 375807 050810 436941 235731 686753 158335 883867 872489 299156 080059 655267 254433 677394 664618 884632 044834 757259 674909 163707 486879 316994 841241 639669 754186 926949 196979 592585 465624 117003 718048 830545 898595 984764 219290 375447 566873 379394 104123 339016 437128 745688 460830 104459 678781 263852 255676 351049 204540 261256 478323 231427 155915 006079 826123 072003 091752 971682 952207 477222 264336 154970 676543 016727 751757 356897 089463 814083 341288 460017 402600 487952 417899 096307 911049 062832 996580 574425 678709 983694 982399 213815 200440 111758 689039 998480 546429 541375 134786 786010 201718 877391 047800 436420 034535 485931 624722 886595 314257 030869 043161 368985 743701 841542 407692 247876 202796 128779 564309 617011 760644 237303 777720 260696 715349 140547 492653 664627 656031 041087 300336 882651 797776 878797 409597 254117 389695 631064 774355 928727 092173 705237 032330 710229 271534 616134 353481 000559 289856 106891 549142 783305 010708 820363 202874 882804 815404 305985 003285 608777 207054 170314 446194 979328 126767 883134 217851 397900 185459 145140 128522 575401 973113 997392 572948 238579 060847 877108 670887 105055 701693 870731 560279 253019 487885 428061 132151 802309 609467 383420 988250 811957 479337 169554 983450 056647 813026 645215 706015 628508 242990 542469 299029 545029 397195 458275 510296 975312 946667 939949 866998 135695 521945 092220 854986 229523 665769 501602 748272 487743 464760 603595 117942 658944 690674 441415 779356 000533 606881 224469 334042 261824 406191 060173 967156 631603 393389 934430 798389 323338 823624 409871 711328 572572 066862 465471 749175 933773 099239 625725 355685 367140 089256 020399 481614 880218 028739 838626 427152 370484 145593 018497 375495 248166 356553 826179 515825 880309 963810 678549 537058 975772 054626 834888 523778 468610 038569 324209 138048 678733 333465 656977 288413 121887 595908 193983 528978 612479 192205 258300 506425 471927 879159 121610 569649 143896 648003 440703 718688 005244 296618 731240 302748 440264 747218 309656 379436 171217 737775 326745 971812 806535 432221 381428 701354 724113 206681 364521 417910 868416 279985 553669 625835 367717 428240 671043 985905 205030 447247 629658 455093 547090 533864 879911 946818 981228 910949 484907 950453 648728 624753 080684 489497 124115 440805 931201 440278 212002 540147 107829 753935 672565 112488 638481 100081 753138 341663 063184 125544 600391 525549 915697 953223 740524 077144 960707 440152 401920 417614 209516 961007 725996 029888 746541 240885 715774 569219 958582 063738 819987 503825 148834 788015 402936 915871 062797 386560 494559 929348 337550 727929 250550 098916 982527 118812 288387 814069 904253 226081 366775 870060 955668 765319 811658 809577 638574 344195 058539 717045 943528 422799 471405 362913 761272 538692 395307 068276 898400 366863 665077 945980 160076 497938 738114 530769 821558 134714 490998 941168 300810 538727 905517 096034 381002 258964 321988 361067 073622 576692 119304 420734 608515 580634 691491 926979 116996 622171 679559 300669 126343 864240 184581 010861 297363 149029 208559 334975 277194 315229 348746 594526 761511 606431 958576 590194 517640 139293 448316 834448 395755 434167 734080 370153 111582 723911 173660 786383 661138 802860 031823 716158 196627 700169 278384 180135 453459 508684 550306 541984 357446 634700 051657 247585 388573 687502 046744 131654 399843 484013 097613 060784 606646 806920 262531 401507 966397 238893 753173 375452 613518 774497 573729 463923 863061 874343 124612 173766 906019 122297 108550 639435 531063 556655 812127 075374 947866 858924 339462 093970 134517 468198 826662 557786 386053 536707 368938 267611 399387 561578 150234 769902 281137 070934 267674 723706 540234 348705 830699 155672 964455 984383 692102 617409 377427 516294 261986 957984 852886 440691 533385 123651 764979 395859 735200 953932 408362 152408 438195 587587 741157 396219 837818 213318 316061 434548 569920 106523 055756 630452 288551 940661 077140 481074 400747 342860 270354 031315 877892 876823 559767 866304 452976 413822 199483 961417 759450 832899 729980 567831 300602 779621 424839 597651 215137 746720 287432 470934 047455 741333 367515 494057 756415 170762 750817 634703 536464 796882 653797 103624 561285 335543 039906 049477 536662 328471 386358 700028 271758 001893 444592 558530 949298 179528 946834 363088 576588 482495 436244 624812 251173 261444 264863 201082 253858 116743 477590 660876 001270 524679 679451 613417 040865 150625 565426 606302 432447 495138 675870 069750 021263 261216 754199 884134 566260 715350 410295 297017 286721 222602 916677 314179 946557 880840 380537 761739 768713 578334 847618 584562 422018 348345 331727 634397 672314 047220 766743 037701 686721 762217 149959 271661 930558 774182 229898 324400 524315 543722 196744 860359 125772 062621 960042 172638 022012 922981 313477 732437 388951 966899 650820 072376 014010 458255 038776 577867 862254 135077 037939 591887 124057 868873 260417 555502 946719 376393 920752 750123 513203 227499 538504 824448 819393 359587 220999 998920 839337 917179 644912 859133 412984 078173 630857 493957 537176 826649 591590 587739 091710 642057 034922 545297 719554 356217 273377 941198 578047 644194 658106 848438 088691 344344 849435 137995 437020 620050 493337 870293 026429 498913 487518 724162 621871 443058 697054 705609 865142 348913 090240 221418 555724 930706 060740 679357 951084 964238 056355 698771 851113 230980 971034 309564 166444 420346 256490 078538 090059 353879 281921 753462 433478 330008 929451 372249 727087 159366 933379 015282 881262 286707 228008 633878 882379 731223 877719 597243 420055 920258 023817 559332 420872 029059 414756 195699 931363 569535 824884 375408 451598 497958 620958 573613 245945 405103 120099 086401 907288 221745 417021 192373 570234 930896 057498 965955 222284 752739 399595 124801 368992 472613 254784 063847 148936 911792 938577 759030 612605 792033 488860 478960 091286 860087 385423 134683 801281 434238 120983 195235 940801 278065 875010 996303 873932 715340 723007 704515 606441 701136 312927 017066 223358 526408 954128 075605 341654 699937 945994 452964 202470 895172 367160 493903 658065 068076 106084 557092 088447 499315 676318 857434 014532 848245 417258 040454 685547 883241 097511 372441 955144 926281 351391 458818 423119 635290 258508 121111 588072 284873 437855 771316 554439 432981 617923 010387 864092 644963 211051 211811 569928 461339 626662 101906 149584 826008 141772 155192 438633 483023 217097 939994 780666 678187 673083 743412 516696 883832 801445 364276 203355 948248 047263 917172 627728 723614 149748 166477 254962 851992 936641 890715 844739 119628 197170 302487 040155 526205 413609 345769 671875 006863 697013 897831 955204 190707 036401 393967 007598 718554 257073 115254 388806 014094 369801 546705 240467 610665 838069 786297 214444 270412 413417 220437 060507 425095 274016 795323 614312 983851 929361 648478 493593 994712 140646 384490 664090 497108 645347 273902 337989 242278 803901 344916 788906 913685 948280 249458 707274 237084 584203 258573 272655 897494 913083 567872 672873 892055 534393 015663 079626 371661 741749 628305 584295 474628 811927 692869 477435 123918 997436 416381 161298 626545 167266 649185 680178 754947 070986 623491 347464 195290 056682 631986 970375 058385 012547 654105 553029 371566 358026 350321 865163 522953 862655 872369 709801 218053 758801 632774 045608 344174 095968 699484 143565 238893 051688 186777 399922 104738 813133 070478 179244 326864 220108 328228 466534 783994 403324 698595 437699 647087 186869 676449 355607 043971 448154 563497 254003 374353 / 313 > 275741 [i]
- extracting embedded OOA [i] would yield OOA(275741, 2872, S27, 2, 5633), but