Best Known (123, 123+∞, s)-Nets in Base 5
(123, 123+∞, 104)-Net over F5 — Constructive and digital
Digital (123, m, 104)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (123, 103)-sequence over F5, using
- t-expansion [i] based on digital (121, 103)-sequence over F5, using
- base reduction for sequences [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- base reduction for sequences [i] based on digital (9, 103)-sequence over F25, using
- t-expansion [i] based on digital (121, 103)-sequence over F5, using
(123, 123+∞, 200)-Net over F5 — Digital
Digital (123, m, 200)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (123, 199)-sequence over F5, using
- t-expansion [i] based on digital (121, 199)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 121 and N(F) ≥ 200, using
- t-expansion [i] based on digital (121, 199)-sequence over F5, using
(123, 123+∞, 511)-Net in Base 5 — Upper bound on s
There is no (123, m, 512)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (123, 2043, 512)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52043, 512, S5, 4, 1920), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2460 623976 878626 244661 841815 801096 533415 360772 849327 385342 699093 974175 389202 466081 230235 863101 537789 185377 591438 279520 705346 805174 757607 320297 067326 343920 581147 955766 271148 699654 822527 420938 617781 578788 128490 632831 098779 114025 773331 178579 676351 947831 525102 122007 453555 401683 218289 369441 236762 638773 998665 661843 198818 000286 611305 812715 830378 456349 099814 773041 652321 300026 134919 241328 831899 916040 528291 217661 378865 853429 948139 782712 600285 506189 653677 809215 950047 801466 918605 406804 735131 931619 546397 120313 312836 455136 940983 587311 373544 011813 419343 952781 762078 747055 410839 177069 492430 889210 093786 959628 150786 205913 915362 554031 977395 704951 896962 918699 145385 199914 933300 809423 196747 699155 430451 226469 281710 616255 001243 377661 471584 428544 349105 287953 248594 802649 436327 235607 101378 290692 359465 525695 072593 734659 147558 798987 522850 598036 303245 465124 380402 843111 845349 852922 609945 794295 602017 016176 485561 831555 550429 366180 743797 145507 583490 300224 259394 632709 754468 198434 498470 114617 076137 162166 645062 714108 248103 865470 305994 905991 336709 582361 667751 714814 031309 512897 931862 131830 189736 490762 527264 915224 524730 102450 923010 945168 547444 056233 283431 815047 647064 858018 801798 145742 412878 608171 636442 170352 764277 937481 796013 099181 723274 449507 232749 004150 040630 200906 377032 110686 985366 760936 584106 033188 205565 115266 338036 200039 825256 003303 450544 575568 133598 902110 112138 156618 476409 137164 308850 278555 801302 030601 497572 437352 800989 174284 040927 886962 890625 / 1921 > 52043 [i]
- extracting embedded OOA [i] would yield OOA(52043, 512, S5, 4, 1920), but