Best Known (94, ∞, s)-Nets in Base 27
(94, ∞, 324)-Net over F27 — Constructive and digital
Digital (94, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 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
(94, ∞, 325)-Net over F27 — Digital
Digital (94, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 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
(94, ∞, 2505)-Net in Base 27 — Upper bound on s
There is no (94, m, 2506)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (94, 5009, 2506)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275009, 2506, S27, 2, 4915), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 624 045517 780553 538090 531557 252817 361375 753658 464061 573103 041796 318857 502938 630696 160849 520090 349428 763959 961358 172944 652191 356816 091391 782120 339429 109205 012460 264568 952022 567010 385460 188110 698864 740245 562058 763048 430581 595095 508745 432040 457699 871194 441760 822558 759239 841158 668132 442135 774028 428732 087694 387784 612569 868763 740950 872964 269658 523112 329251 538014 917809 853168 609922 207171 650525 802664 396563 240814 701167 497347 856001 834696 116435 474122 480889 263222 329167 367046 052852 254555 631049 162770 850846 138324 891935 648104 382770 007740 303089 067247 181698 288720 449138 761661 913355 719645 400115 941242 837993 861284 305161 933807 872789 368805 187317 631581 356495 721380 825138 296270 023280 856794 417087 002604 253523 209499 659816 822739 032976 363952 632791 367085 168291 114132 118291 688982 155497 136645 987037 442902 576449 888057 042290 227630 644968 352110 411507 336982 390180 491817 133126 872093 771000 291964 334980 437308 342761 217852 987241 781839 405007 887529 661530 293397 981038 368443 592055 189825 575260 233114 706280 183148 384046 946371 155354 867431 410632 812154 445142 513726 691882 908644 123231 134394 465227 338758 656913 009374 141118 475734 403512 101770 652576 706804 986055 938985 814532 366380 018342 070617 012252 084390 964991 883246 039305 277233 865288 947480 597550 143289 009979 582873 451068 672499 127409 230737 526893 206688 639593 834590 004365 977256 173909 704309 635120 699657 231972 918657 957370 816281 496060 574311 270480 615562 394678 239190 311527 139940 269564 719615 956225 387580 992299 367135 840030 059119 202334 976806 952131 146111 659304 432262 870139 634237 120298 234280 516944 998675 232918 660823 996771 886262 585469 105068 196602 176879 726491 954526 050891 010007 905269 819684 693699 872776 221176 914692 130588 933248 782342 812588 393274 334138 479451 389187 594675 007582 636592 074285 626964 500594 858340 447800 699702 391124 108174 503459 989767 225238 554133 147251 795082 326872 171726 358558 049837 018196 894453 704129 107464 414684 209701 741114 807668 488825 568329 262399 841430 739906 028365 368722 493018 703475 001414 605380 900670 178166 374421 202592 890277 803071 365510 414398 641899 733223 039162 883362 729098 780424 912008 612876 290276 552019 066492 229332 325223 369638 823299 032156 344109 546113 223127 705003 150542 961048 189757 771369 360439 217502 826134 995298 973644 169386 324529 881918 830713 220301 914152 005264 914463 085071 578546 348496 828512 534587 048305 823203 462345 243575 107622 965449 043573 166609 825202 082768 866251 993907 247528 882526 900235 874744 667160 719710 419112 403106 465625 914096 192634 854028 993517 912485 896013 115497 812327 896336 719579 522885 017290 209116 811973 397622 141714 459404 669929 662059 487415 338516 216349 617674 308304 673530 694013 067108 996885 379476 484577 046608 255077 918206 973355 453274 296596 699425 613083 727906 380368 660171 187962 514789 404470 503621 993878 819159 751056 976765 308658 101181 458574 749765 027568 040380 375442 723305 881280 651032 898385 194991 591893 289326 031493 982166 795392 502629 752348 942424 664566 529497 798055 257713 719711 562760 645291 906351 737413 816582 692651 733614 242708 222160 993646 669197 206112 120243 851446 966932 405762 983390 384510 952779 539740 434490 866819 515617 816487 350801 943096 677685 262357 227843 214030 020937 505049 947601 349722 234572 520325 598289 187602 954868 121157 535883 947618 370215 979176 908100 150804 191576 910030 234707 988813 116011 750255 105853 447814 950514 724133 643483 235781 741878 365724 936947 978266 672277 867101 936393 662486 171116 337574 941059 676843 942770 430283 362251 773089 408777 513363 648068 945249 206155 144250 356459 417055 099000 020588 636241 847590 223761 108000 402173 139476 794706 611513 380631 390468 969822 135318 053838 257889 169213 295820 367524 383629 207520 524752 792233 215828 248309 221943 593532 774269 510102 935748 426495 235383 970021 869316 162003 634880 206992 301268 603586 122972 237216 934478 147493 676397 495217 894342 761607 170880 616628 974948 581836 324226 354823 203217 074344 180750 476804 266530 748516 740024 111318 766127 253081 178369 963744 369902 446304 953538 455583 515025 550171 637444 068816 656900 711412 073876 002544 462976 324274 893375 151278 554311 710288 493201 045690 039129 883947 699864 248738 087693 559453 252930 427115 364867 834544 200347 471722 327959 292312 697786 355578 567857 977198 266683 749016 284224 419576 228829 159549 891592 267876 615842 133651 675822 705331 695965 924505 531585 095008 030500 774736 827026 609928 522528 941695 762009 342338 226052 096063 288005 468574 309276 793471 271311 914445 765307 177142 876772 623664 742510 663836 925521 439490 623850 755751 225078 871632 040035 519644 513756 183067 378129 165720 711950 556711 367706 360677 950377 271204 018884 190690 709038 008589 334491 617554 682098 114086 050185 424250 666759 953926 562748 465576 790600 171616 188833 167049 556604 195273 709230 713703 487599 494319 325231 200067 095418 114145 418160 596163 682331 411467 974042 082994 101748 114720 147514 633361 878657 371711 504080 788763 067629 760599 902528 016125 228969 568738 173216 834432 136248 330950 708085 668023 054043 733216 585384 107083 065569 953180 021311 492516 414403 913282 358229 778998 475237 381052 464239 509680 572017 488247 844109 271540 628659 756945 595866 095803 203485 568102 217983 930314 197870 698297 270339 518177 446593 304057 693159 216198 817706 925141 008499 772556 004507 927081 868426 321390 040947 981814 503231 567454 304539 924979 227678 038162 021821 234949 133386 499933 168288 006853 001816 473996 687597 329446 752687 586760 380085 174793 177676 272100 203560 339929 079043 984165 541659 869754 195528 886265 099936 725720 469800 568660 472992 442079 988142 250287 916895 431316 105930 422644 806481 717151 432560 002957 032115 988284 050741 882653 459308 871894 333840 774409 921763 471684 787494 718216 856775 626649 648166 866373 296481 467890 084799 543125 391648 845119 064672 248830 216645 814682 836858 296348 161440 096384 120127 528559 986383 024976 192399 370573 352082 799534 831856 807958 145450 490324 619660 652362 688699 775644 745309 212873 666286 110735 432446 665158 914175 127641 737137 084428 770389 782514 458461 237043 873304 797298 720851 777836 111239 575743 005786 335835 152977 925462 843224 512772 418773 942039 337679 231725 977335 382533 066143 352616 685066 259177 308720 145496 212479 843648 154903 251828 999375 632373 177889 633102 680599 272871 315952 350930 348134 068943 851252 822811 175144 479348 533337 829346 702344 868956 031861 851296 377466 276566 336348 735816 054146 465716 890513 861609 096322 410228 357167 666581 371394 259538 246430 611155 093772 822228 662656 468491 417182 149134 149937 386296 020825 032806 644688 336565 741061 222409 630036 864818 071178 472435 681799 213354 425161 060889 321564 730802 500657 176729 388584 568518 678586 599627 495479 334039 494103 367689 552427 597357 461493 856734 895727 722382 338147 198456 452274 737089 920495 756503 586913 843698 666706 041515 942057 493127 417621 513591 716967 832270 680966 002406 376053 797246 877369 266855 864892 361971 848208 700298 362362 377871 046722 636611 573437 110628 735112 972336 962316 880432 865654 754193 991199 139294 069250 866319 549089 514994 672541 945109 099453 673276 220189 814173 567938 768338 805183 404715 859651 832489 217069 459982 179098 376497 992610 477885 782725 108469 995864 373719 473620 436405 646048 991618 464461 644469 998661 887987 210137 106067 517267 712418 291051 873811 070175 346264 668022 461140 806983 818718 524828 210633 653486 021474 923415 384536 224432 190726 020078 761504 641138 093562 480708 530864 949580 753842 896137 021926 802718 910675 660692 582139 092983 388146 797152 705621 856079 284177 405127 310729 591053 720474 323268 244134 595460 247611 822652 939234 971180 384155 066642 853107 999352 292697 283286 668634 956350 253013 752372 273042 968810 961303 852871 238276 844285 617656 103964 640014 635288 642564 505124 082664 530489 594234 729671 716258 774406 598409 773207 415728 520668 366138 065083 899682 955373 580392 296918 175613 040595 216375 479986 510022 253448 952691 841012 931243 427775 448995 330233 679485 639867 829461 072471 974383 462733 891801 852743 065135 785344 553854 / 1229 > 275009 [i]
- extracting embedded OOA [i] would yield OOA(275009, 2506, S27, 2, 4915), but