Best Known (22, ∞, s)-Nets in Base 25
(22, ∞, 148)-Net over F25 — Constructive and digital
Digital (22, m, 148)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (22, 147)-sequence over F25, using
- t-expansion [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
- t-expansion [i] based on digital (19, 147)-sequence over F25, using
(22, ∞, 171)-Net over F25 — Digital
Digital (22, m, 171)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (22, 170)-sequence over F25, using
- t-expansion [i] based on digital (20, 170)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 20 and N(F) ≥ 171, using
- t-expansion [i] based on digital (20, 170)-sequence over F25, using
(22, ∞, 578)-Net in Base 25 — Upper bound on s
There is no (22, m, 579)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (22, 1155, 579)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(251155, 579, S25, 2, 1133), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 104 387867 316352 370745 269036 490997 560027 658474 707564 425602 679290 247239 557444 271046 140590 446041 809771 543165 491388 156244 955004 088165 940475 290398 461828 976171 349881 672373 196861 167111 853910 216760 279352 736159 689935 370366 771072 229429 797512 417470 995877 660532 920932 185416 222977 348430 430069 900920 378617 801582 638861 785024 797258 040113 092847 736464 973391 356213 833384 409747 148382 977362 010337 074042 625280 067972 648328 670452 710959 255316 812502 962414 330806 257592 721248 142251 504803 002238 637864 266187 698698 932233 969279 707897 580986 737260 798610 276730 587754 028704 927745 811033 464708 805245 838458 107451 701997 643636 227255 455024 690018 186616 168781 583002 465372 649511 352421 011598 946997 289715 527979 912644 886065 701141 361001 073015 896918 409907 548321 508966 513354 185330 000662 183563 489054 733693 389236 924281 203773 615040 413732 791564 213846 824818 003031 309737 731108 754727 397453 055885 570832 245353 669489 447385 849281 474911 680396 496632 768633 560063 998439 102283 487393 198180 270998 051359 975345 975252 601248 645162 530624 732852 111320 224596 997825 795943 071585 251506 880840 052542 417295 166200 925188 212529 961799 931112 899889 030759 863042 774070 633939 926751 447121 156635 497472 411857 457511 339734 319941 977691 050475 594124 669077 305162 594414 481020 560080 823510 782289 058812 387125 533660 773580 915357 371412 181433 991959 956192 115198 760214 141433 475319 858487 979074 939102 023613 591427 613561 487864 247183 942295 562407 603320 410846 386805 138849 567238 541956 349796 289422 011971 731995 550930 841928 870090 919287 381615 139758 334780 097772 928940 325493 145103 546535 624914 693309 821883 018027 512400 549046 914005 752792 158297 138394 520534 450639 835751 105536 914904 908774 105091 716306 992059 327962 696357 872118 824161 589145 660400 390625 / 21 > 251155 [i]
- extracting embedded OOA [i] would yield OOA(251155, 579, S25, 2, 1133), but