Best Known (98, 98+∞, s)-Nets in Base 5
(98, 98+∞, 82)-Net over F5 — Constructive and digital
Digital (98, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (98, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(98, 98+∞, 160)-Net over F5 — Digital
Digital (98, m, 160)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (98, 159)-sequence over F5, using
- t-expansion [i] based on digital (97, 159)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 97 and N(F) ≥ 160, using
- t-expansion [i] based on digital (97, 159)-sequence over F5, using
(98, 98+∞, 410)-Net in Base 5 — Upper bound on s
There is no (98, m, 411)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (98, 1639, 411)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51639, 411, S5, 4, 1541), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 124 777691 371610 773387 837965 013019 032234 421956 898413 921434 198326 003529 222580 038147 203606 545272 058452 975192 971971 286922 837797 272278 615051 781584 183090 352846 720658 884684 702084 723193 220060 229738 091611 092091 838193 988837 524303 183126 109801 264869 247978 235605 643406 211996 529830 126807 698889 736970 882630 231975 474957 967617 680148 544259 382606 544391 749398 697543 078857 680050 186613 935947 686127 270030 974931 532617 773720 113605 359169 277728 502804 156637 476867 838491 606751 389922 020306 912913 751114 656349 687125 835248 761807 919901 234210 122923 301412 547722 297129 809560 869842 809699 008655 388107 921930 426535 455929 451729 487759 520338 450983 801051 092223 535625 894759 620479 122471 471499 560435 368118 745865 791627 319258 961285 168606 949838 258098 658290 642020 380251 940423 513059 712030 321685 674660 512490 271307 098941 173506 569242 934376 841160 493653 077784 240162 108843 114778 062353 536475 230429 896897 939532 978916 725957 432611 904975 465419 866483 103494 148380 353319 546883 275342 457467 688846 897107 118545 626103 007777 339655 426735 487491 909975 738799 376889 140136 713749 597730 558186 593316 103621 244271 768119 183379 627482 416991 534167 640236 753859 629061 585031 941418 757783 092976 525640 867280 220192 014894 564636 051654 815673 828125 / 257 > 51639 [i]
- extracting embedded OOA [i] would yield OOA(51639, 411, S5, 4, 1541), but