Best Known (20, ∞, s)-Nets in Base 25
(20, ∞, 148)-Net over F25 — Constructive and digital
Digital (20, m, 148)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (20, 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
(20, ∞, 171)-Net over F25 — Digital
Digital (20, m, 171)-net over F25 for arbitrarily large m, using
- net from sequence [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
(20, ∞, 530)-Net in Base 25 — Upper bound on s
There is no (20, m, 531)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (20, 1059, 531)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(251059, 531, S25, 2, 1039), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 917354 568318 706056 763794 758314 379632 821429 439601 950538 307440 502547 390725 907471 137645 153823 145907 989825 094533 672442 834150 647426 404438 285149 594018 803141 198596 530127 518056 842586 713071 289596 090603 562509 462755 132739 211488 976690 908210 183749 065142 191540 083807 937501 039756 256757 937872 599230 559257 517857 100777 867542 415724 022392 456677 914987 093561 411133 774514 927907 092008 351906 572428 402261 204123 623888 366881 977816 883522 809707 086117 990974 041105 292748 443029 514008 871041 570713 903444 828861 615229 712930 331308 269282 012156 562291 339188 432474 340748 419327 115738 946732 528821 356738 676350 939857 409143 861082 310659 780950 041239 052591 117272 832958 371843 761230 865040 718090 244747 174513 035914 270735 444233 372087 124562 116862 705843 942030 091498 450055 245232 327649 891364 141560 576822 884282 943507 877123 568530 174052 097914 444779 627256 522472 791331 853532 691789 166678 311898 987323 432214 026768 182965 222467 573326 045233 678774 177863 107860 384023 473129 719333 538636 023594 901640 538183 190753 700894 616172 979780 542692 183449 676377 323839 029750 399143 470001 196110 975690 209742 616378 707579 109823 893912 832191 386178 930705 167795 884246 888044 460073 377120 651502 968931 568713 991614 559994 210770 545250 250255 298364 097933 768668 287661 724761 372523 459922 991959 214345 212147 157871 511877 612942 158829 851080 885462 493482 859853 375998 702204 434558 604047 528585 107616 021888 606736 365465 640318 195145 851610 409127 139866 038347 783586 846831 886897 817111 961221 200444 462085 926850 109748 851312 672083 891172 952325 749381 278211 426446 814477 118972 368241 411885 492198 052816 092967 987060 546875 / 26 > 251059 [i]
- extracting embedded OOA [i] would yield OOA(251059, 531, S25, 2, 1039), but