Best Known (92−80, 92, s)-Nets in Base 27
(92−80, 92, 96)-Net over F27 — Constructive and digital
Digital (12, 92, 96)-net over F27, using
- t-expansion [i] based on digital (11, 92, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(92−80, 92, 109)-Net over F27 — Digital
Digital (12, 92, 109)-net over F27, using
- net from sequence [i] based on digital (12, 108)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 12 and N(F) ≥ 109, using
(92−80, 92, 1164)-Net over F27 — Upper bound on s (digital)
There is no digital (12, 92, 1165)-net over F27, because
- extracting embedded orthogonal array [i] would yield linear OA(2792, 1165, F27, 80) (dual of [1165, 1073, 81]-code), but
- the Johnson bound shows that N ≤ 690212 096321 771801 287464 537326 693449 391029 847949 635893 612729 256707 916396 719400 053112 572158 273003 193226 870278 474756 095496 714385 138603 727843 690674 391061 182437 677371 829788 281451 813290 641589 405874 387470 187579 621994 459539 042515 507944 014685 358326 016337 062649 644234 492102 356499 800742 549663 955243 285960 896102 886013 114127 868425 553146 894199 965540 033138 457508 875323 007140 635461 982172 938558 646865 798231 501276 856352 904430 924614 864392 217990 370906 997355 664756 856252 902128 391518 069709 147042 484459 855547 488300 187256 163382 429791 949231 480427 039802 708677 824543 298298 053368 581479 843433 951779 534253 377669 780453 764878 707598 712404 663699 440648 616723 931599 897773 406749 569513 261391 198645 065778 851937 294819 179421 335598 656107 032067 666977 163408 763348 467435 923819 955982 988923 534170 164308 027622 951226 869009 202136 928965 323696 717325 959602 849987 949908 565303 470554 917020 361105 775873 852318 887390 883909 774809 677796 487538 833193 942801 776215 488725 637035 633203 827362 655907 998235 607747 046079 601379 146582 294203 097933 696644 196910 756668 985527 206296 524522 681476 731069 300389 661180 428941 827899 584674 672454 409646 358855 719339 012127 860114 448555 158852 134612 755605 702025 472485 952235 712206 441892 863370 103181 265779 441994 370122 419650 189724 835502 858011 923318 404368 209453 820663 518258 484260 972489 155692 208375 858986 778699 999710 594689 254153 882698 906439 018800 606277 400356 169139 623022 765113 932097 377592 704396 712655 091924 337960 650693 040762 601037 626796 471522 550343 376034 571574 837682 084730 494637 022612 737541 524728 887456 002840 948777 502067 351264 988684 835304 280321 951021 421549 920572 870136 547447 952395 239786 < 271073 [i]
(92−80, 92, 1167)-Net in Base 27 — Upper bound on s
There is no (12, 92, 1168)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 494228 442521 187049 171786 563981 263677 311824 565598 009981 528865 816886 584513 391146 601778 809564 490194 374467 227242 970224 017453 135694 379009 > 2792 [i]