Best Known (106, 106+∞, s)-Nets in Base 27
(106, 106+∞, 324)-Net over F27 — Constructive and digital
Digital (106, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (106, 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
(106, 106+∞, 325)-Net over F27 — Digital
Digital (106, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (106, 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
(106, 106+∞, 2819)-Net in Base 27 — Upper bound on s
There is no (106, m, 2820)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (106, 5637, 2820)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275637, 2820, S27, 2, 5531), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 20 307475 096564 897840 757834 256551 032588 269161 886443 561979 430153 849232 055160 125831 373762 742689 592111 076425 459919 724571 306538 766750 576963 987736 991124 154814 834084 900130 904303 322521 631158 855720 283815 119091 526777 706994 149355 928158 876804 834793 840152 651100 223064 676948 538405 431893 233830 687728 570269 162758 439709 109609 409959 093956 393574 848786 316221 858934 036663 424194 957585 802900 779986 721583 081468 322412 774264 001791 605575 400165 403623 445691 946439 326977 991050 355908 978990 463898 042955 519819 849615 473000 879005 320201 869580 299488 605734 636234 770714 763481 565830 005939 012064 081781 969909 937410 245188 725256 635771 056052 122673 387066 693623 052422 597964 391198 799039 054764 787972 117521 975150 373096 435780 056427 588136 193857 153130 513403 663283 513250 826009 162614 638451 657413 637399 796268 305221 813192 276760 001393 282590 916658 472402 906686 232476 628130 592725 598778 378078 929602 459281 627783 041800 508049 503426 421321 308378 086343 546374 323486 541453 959337 911438 553101 205007 584814 608112 816165 755908 915204 193750 024119 145021 951201 984859 373249 177894 872723 813422 924986 347902 170074 349866 794046 639108 662763 312480 045322 290388 985389 342845 739542 350370 393547 602910 076193 583068 583392 226033 185367 695630 085359 781265 276174 979351 954174 074388 574930 250087 680719 201097 846310 480942 172226 760011 380855 037221 020282 025928 206572 428679 736693 479521 652612 232726 727597 054992 384402 771391 569801 188278 613533 296551 574139 712808 505478 483633 468852 671333 743059 391838 808896 572433 523207 141714 117767 662788 720939 009673 134029 145704 332320 229666 064248 818866 267100 127781 524158 337269 228402 961795 947512 970877 090757 625643 047506 823485 564641 016444 492071 710944 564790 577060 631587 861225 349955 080038 714844 055842 787332 171542 595467 843809 889555 350016 180391 785179 366965 673242 303275 457797 206656 673917 394475 286501 596425 685905 007737 973729 079579 664335 613514 086322 058163 129443 663104 111447 347711 299539 608545 529885 820706 179323 849205 205695 508440 181038 350011 866161 936237 073375 815721 898292 097430 999496 974039 674140 690481 587711 558114 690039 961673 478186 431903 479358 775386 421242 140817 450353 377721 807056 962940 450606 075307 220240 312034 669881 999980 943827 823702 030830 070480 554301 563871 738556 241931 803089 697468 448744 176202 927754 122380 080904 299458 356327 291302 067683 765768 170850 688246 726283 644319 715029 682806 760989 383654 408689 089427 549889 055516 321009 252930 289110 578874 836680 871743 476837 527771 677625 865662 374205 170129 125518 142302 408731 380092 928044 119404 032337 595032 648560 793797 128068 145386 083519 722078 735718 069506 308475 453285 864482 365710 447102 445666 627319 625673 671436 645884 271825 523342 594729 412460 311528 294280 847497 161868 914169 316006 711454 952963 423690 117069 665567 009210 235835 951133 332001 432979 257986 714901 212946 142836 957180 900507 079757 543768 470000 456685 684487 110143 667140 537690 082599 629965 809003 454715 307144 850362 009866 933696 090634 180319 816997 731624 327992 960292 258449 965005 082409 212899 396511 894415 532556 039984 529461 314450 395053 951918 301215 065688 355875 588434 153986 214888 380670 187998 354927 864389 589689 181004 436148 185086 050312 742373 762501 271536 459794 911946 819871 406546 348707 266707 008854 235279 095927 583749 688209 914382 093242 722510 235462 896962 821025 710962 180342 393079 644609 636487 869003 087218 568455 843491 725041 228279 532324 675031 726284 198494 750595 078742 426796 536212 229134 275409 417383 922485 923000 137673 927706 464936 650004 046905 668896 474631 233986 515135 229152 677674 047992 508830 123886 728797 823068 346162 386273 507382 454013 983526 205836 570988 104049 560506 303285 459058 083878 165463 618675 284317 441823 084874 405429 944078 534704 407259 493939 715256 284350 916653 503133 286905 706458 960606 075435 015858 285350 013628 570216 284352 949349 354235 807533 815551 470148 027224 350186 135882 886538 073408 624951 518856 078478 360274 695764 421219 108446 457565 820962 673474 517203 369743 388084 076724 393899 323871 011800 487746 592854 047583 051190 783132 752107 215445 110054 054649 543451 256588 086308 228724 113561 076886 917901 562873 358612 070084 047960 580720 185638 571478 233190 644665 572140 754628 856095 218841 448753 708339 258132 164874 785200 868195 376022 406523 985769 919828 904099 199797 499873 236385 533106 431977 180185 112617 394073 079521 365187 075176 214973 644797 487088 629614 895890 126041 298669 422164 060386 590162 266741 909289 603519 902318 588126 003817 619288 730852 297292 110824 991083 653963 440027 152935 589009 897145 062129 376561 706997 300889 446203 721648 466959 822116 867272 532922 034053 781349 001627 138155 902525 330502 931017 995510 408490 791268 411795 181513 854226 557250 886141 365644 599558 220578 955984 659873 269683 371337 487226 090835 641295 669322 366563 790924 325705 088653 600886 730236 119599 454412 137111 127737 368363 429788 367825 357145 316878 565748 009115 727350 839567 207827 411210 297432 647363 482578 027815 959064 328739 077351 003779 041407 911523 253033 385006 220877 006289 834457 239327 178753 601408 714952 276006 908299 054074 704275 421282 323036 505321 892008 422079 108722 330105 042566 410381 945767 330024 801996 073339 043173 978476 907572 365285 288155 884086 954441 115664 408315 015135 924246 901085 814126 936212 087270 337470 443427 234130 077040 439125 228155 238417 922469 215725 521585 866844 599867 565128 859006 295041 582328 474687 504204 410020 491181 983581 539178 742610 794171 385785 863330 087373 174499 396333 064665 031069 958677 231383 993076 289719 248495 662739 544088 668381 986458 454787 498726 775801 855214 740520 046468 462957 997643 961151 800073 049517 518813 384071 086524 052598 055841 572010 748502 835837 424378 592996 544401 273304 042554 434242 851656 996765 914840 460083 303450 076920 735450 830383 256430 633321 056831 440033 896151 848656 003048 051953 732720 758613 753311 869316 650231 564722 951809 874881 905283 023788 684040 985899 514341 894369 439503 577050 058762 774112 577449 502342 374223 097538 688200 086028 303591 017927 566617 719206 114975 334635 254425 140200 873294 680198 884178 408242 908392 843388 009035 837905 323181 565191 599518 756036 943604 708059 889055 905976 001119 913966 770949 460206 113841 505048 274787 503781 303283 528862 356909 043712 996128 764321 373814 068987 792206 358569 118852 640436 443361 918369 815873 770357 501328 722870 790002 593306 861201 697111 288267 325114 906879 823849 052595 964833 420528 720343 529268 339925 318107 377477 625707 580549 103868 764969 420891 902656 512662 481780 171624 150914 360555 322732 518434 799546 750601 996115 916321 844625 145535 862531 267151 646844 596373 695790 995909 698625 849309 449856 387652 288201 380483 422381 810385 277975 729232 572518 489201 276713 820854 054647 381226 581896 459640 109467 509462 666363 590652 537465 777325 636362 224018 327078 796289 185899 989173 409204 366001 204665 388188 326943 196435 281894 183407 983669 699779 499480 723230 412206 139018 885872 473913 005581 355616 184583 669390 880614 299247 001185 367080 230412 193805 448506 295175 115499 014238 263375 769750 647682 810696 692309 697641 273481 395554 729108 277863 700109 613403 399323 447056 519657 232128 894208 714755 389767 555165 962285 685564 015352 923015 866817 801769 418474 766581 256968 551103 326226 401700 984085 967636 688306 102771 082360 129639 403600 781484 026289 572837 460460 128470 734418 707521 061070 131094 615759 572336 054565 045115 417668 166917 615966 753942 312885 974130 615034 267744 283010 046357 106602 662974 930489 226100 249182 545594 738368 317081 075746 721484 263035 714989 731725 792309 715600 456342 036642 526449 204118 928245 592116 296508 724029 129126 276637 712207 979757 259425 262257 804887 850743 113092 404151 545692 139083 541783 732484 740725 769086 176010 984394 255686 878937 917401 135032 730233 351580 222660 909071 473574 689892 729282 410715 690360 297858 169463 640783 070869 847131 135156 225429 297418 896106 920841 521743 693159 669503 351702 506933 902876 566698 499157 015286 076647 965260 013020 456333 958269 205968 907811 513999 860405 955470 957503 220911 198719 949950 287709 836667 747693 815575 301888 330295 675465 560401 136265 550448 459419 108309 075444 134852 096260 543215 573841 603218 504198 255456 417505 226703 085648 311904 521220 092442 430097 667054 537647 983225 212525 139919 280264 915960 930684 141325 678222 093514 135083 204942 747444 618175 033947 506196 308787 147172 888856 047879 425177 375770 157472 669730 514426 413763 763343 305057 276612 850984 950393 043412 800427 913058 339041 863086 887866 303586 446469 201972 645226 315022 851149 554631 038153 423858 084195 442730 009761 674063 079498 841338 946119 204300 675952 196873 329709 897671 402653 703055 826344 233725 621946 361310 575532 537983 054785 105659 396188 145181 076040 266584 286278 141029 080005 019900 878012 254355 259506 193420 839792 794060 491349 549419 312924 239362 178078 068566 262908 168631 208702 342422 387589 208305 584118 389233 198115 375870 406265 828572 182173 225133 591490 627518 476382 907821 256994 665977 312205 430625 170145 723145 185004 563533 820774 336256 601159 710089 241553 118022 477156 994533 474411 / 461 > 275637 [i]
- extracting embedded OOA [i] would yield OOA(275637, 2820, S27, 2, 5531), but