Best Known (70, 70+∞, s)-Nets in Base 27
(70, 70+∞, 114)-Net over F27 — Constructive and digital
Digital (70, m, 114)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (70, 113)-sequence over F27, using
- t-expansion [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- t-expansion [i] based on digital (23, 113)-sequence over F27, using
(70, 70+∞, 325)-Net over F27 — Digital
Digital (70, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (70, 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
(70, 70+∞, 1879)-Net in Base 27 — Upper bound on s
There is no (70, m, 1880)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (70, 3757, 1880)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273757, 1880, S27, 2, 3687), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 22068 830060 468089 320808 787913 687789 160602 594007 551050 359903 161301 692174 773194 156173 591788 615213 545050 752939 883713 466980 550971 006278 148659 540073 790043 938560 835093 841433 474109 448257 235617 607136 539828 024292 062320 359000 599341 745079 495127 774858 892486 023459 367111 296958 209063 733084 986873 849415 031750 749639 601093 607138 362760 273843 714957 796808 151733 606959 620478 944739 790189 170900 598272 754142 419183 572264 366056 331029 622490 453041 975581 345921 190541 939241 355552 115791 369151 893477 911266 911537 255969 717282 132011 143305 406963 273977 441828 550799 142043 006129 848802 254784 740350 751041 610848 302459 646948 984475 712464 547941 110692 207380 022433 591758 398913 369748 306094 473825 264962 051894 489095 612977 395343 117447 909068 763269 235706 325971 887018 616838 500674 371510 970859 141810 311910 188061 110140 295560 405161 739634 611249 414535 889950 554027 090057 271351 374098 979649 389903 357235 738688 704237 501856 186044 732812 935023 263240 009977 397186 031255 243866 319931 149799 947566 405386 839214 702647 515806 908153 655339 695432 389449 205496 262736 114374 842589 495840 113273 905144 637473 488930 530493 334853 750274 514761 994627 842770 232582 498659 943415 483329 786530 051648 087204 246587 906779 288319 312029 861591 449400 910425 656396 323966 472403 740150 746518 091551 598628 994647 432694 970385 973216 169166 181544 502487 869449 239061 937512 990498 863465 877842 120858 075312 193958 731506 076403 774474 630946 077706 428726 753698 641712 578789 362028 225205 956672 493116 414292 428527 798206 909148 738825 823599 312557 101990 859612 130527 917730 375210 967362 443108 561982 538631 955952 779915 661706 367470 238549 831662 005889 109159 993368 511615 407595 161851 721099 786608 071665 916916 077800 157994 471231 458331 790603 114552 342252 394991 884507 036285 892264 273853 551457 857804 443357 297910 258023 471832 697899 259883 927027 191456 629960 870359 638433 989902 157535 934392 393622 859797 708556 844773 024715 045610 086790 869955 160004 445503 982116 484147 719283 128039 598961 607672 818210 051486 393713 763547 293968 019874 691217 297273 085468 944311 435443 229081 762045 455715 146793 811777 764186 823293 513884 352180 777761 398995 742316 209391 700144 934487 106992 758390 129395 852730 974686 205357 162710 682337 755958 279366 129087 022116 847164 238997 828729 343514 186935 280717 677282 802804 525435 305393 189252 187458 736106 731776 191945 392919 106716 411098 240091 930490 651267 005867 074904 852743 431141 438215 003703 400452 805869 649708 342281 307240 723742 722086 658342 797621 014517 889332 859473 250844 720704 577404 487283 342952 578033 744759 650034 251268 105942 269248 396742 920694 564550 245696 784160 003274 848307 235807 244790 496430 108116 910386 913407 896628 789824 835060 659640 665979 161792 062829 803318 459298 583279 260649 984705 782547 695569 873424 312780 164532 106307 962783 280689 512507 677026 143762 644562 374615 389938 481661 361541 545124 222561 709450 107330 581033 760195 236361 479735 452575 964212 044901 860312 541749 954828 266060 596643 131549 165921 431000 884230 952512 521926 003343 094541 739779 637894 759663 807684 626876 053757 617707 895664 387679 501913 831304 112098 262805 141634 574837 988595 820339 988540 430162 221160 688375 319056 125543 222944 246750 333682 612410 405659 446531 854587 968432 125031 632658 526972 973211 246457 142876 060679 176775 544089 454962 786893 441131 336917 495170 719020 496992 981786 763595 608853 915601 817504 330232 500894 097562 951163 333174 163882 452996 145078 418001 777254 362583 581201 193181 937305 857055 058437 893692 014228 614520 094005 214114 902128 334008 759091 986280 937796 392506 109280 224009 602548 806489 094592 845902 582028 426129 674108 166493 084020 906016 893706 065587 821450 544606 920452 365661 710091 363345 876587 964110 521558 267195 293201 152848 979085 691035 878151 779950 225173 586585 025855 796563 157228 491871 664784 729715 644012 333066 629710 889323 206377 206946 991839 335248 397846 965651 434603 024671 756217 008930 096977 119592 041322 913986 202641 290434 016916 080518 530955 555629 169761 663287 540977 761975 983906 730247 505353 215122 568737 224058 454549 336281 358068 748983 455494 842469 464521 053883 876650 091805 601718 380958 364887 071086 139921 214268 868725 401934 051914 004603 893000 752092 287380 415062 220964 628174 848090 059079 368385 746927 081365 681327 844325 272279 964861 984140 994149 478538 852289 074119 365567 551859 350898 593803 775187 642366 271276 883676 988422 237652 845525 473973 523206 656975 810319 084111 432411 001891 400074 058469 032687 869671 403809 227517 681809 845727 271859 060402 049314 542136 129519 468461 990360 675905 306459 724341 728147 042493 497666 831883 405582 393744 540456 530755 217427 459545 648526 188226 237267 487205 840228 334928 501865 042897 912420 160041 957957 319641 873311 206470 441754 729602 769299 388458 010122 045893 918325 594940 470652 419593 745377 921900 370128 029320 714752 147464 408394 722923 897454 431803 982532 686266 625817 841822 304896 568226 629336 226112 000056 176377 008176 716879 464368 218714 418256 189222 961855 944935 877081 939356 552269 014071 367926 483645 322034 307957 945345 065401 703245 488206 828097 175436 955197 565937 018919 692640 659391 028988 711721 990237 033294 857491 889314 124853 833900 341722 469767 685257 328503 585313 199044 336474 713376 344441 646857 138316 084581 291098 501677 285984 835435 848291 879456 806681 488469 980435 276343 423624 183769 873500 161601 934573 168802 457697 326927 059862 359633 799905 415903 273619 863581 476176 025606 230934 434509 499271 570338 089433 235815 123356 382070 232822 748783 978647 665752 461704 510846 723407 979613 062466 946856 708103 952830 739908 720509 849973 996235 778437 684874 781449 906263 635269 793704 138880 700029 166948 614772 284775 258443 581644 015845 647024 532641 337256 575457 939257 887812 412114 977877 483759 366402 097253 172166 133141 041421 203843 213458 077729 636024 598867 415065 264441 090498 365230 113319 026425 438871 372194 504516 996747 179206 074130 543567 467749 778422 409926 563080 229373 382684 506978 630539 479570 511964 371269 174235 422249 774579 064355 235059 625611 / 461 > 273757 [i]
- extracting embedded OOA [i] would yield OOA(273757, 1880, S27, 2, 3687), but