Best Known (17, 17+∞, s)-Nets in Base 25
(17, 17+∞, 126)-Net over F25 — Constructive and digital
Digital (17, m, 126)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (17, 125)-sequence over F25, using
- t-expansion [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- t-expansion [i] based on digital (10, 125)-sequence over F25, using
(17, 17+∞, 150)-Net over F25 — Digital
Digital (17, m, 150)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (17, 149)-sequence over F25, using
- t-expansion [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
- t-expansion [i] based on digital (16, 149)-sequence over F25, using
(17, 17+∞, 458)-Net in Base 25 — Upper bound on s
There is no (17, m, 459)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (17, 915, 459)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(25915, 459, S25, 2, 898), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 19226 487734 458668 427348 413082 460983 118495 021246 231834 191619 011714 902587 951494 174290 233726 550473 994085 574766 234508 923288 166661 797953 272897 594001 812600 292682 358667 036613 365605 755540 751744 401069 753592 315175 067674 857915 994369 089468 141275 372527 755511 153004 463780 172580 399233 084307 181217 287666 170193 741912 822289 503687 494444 713094 852230 794543 594896 560793 952784 411951 768268 661879 095598 388714 279573 496187 364933 942191 071094 548477 711252 349118 806090 963374 028294 569840 492276 043186 229138 488622 703187 309137 856764 764897 570485 473119 456493 127198 234888 213655 458334 913195 386748 058292 105741 184363 513573 048657 767066 844554 849813 057381 021279 422336 275573 394857 807854 939656 653487 193488 157587 062200 861557 386231 284571 909576 731243 800124 322668 965731 054828 359456 817075 800865 079221 929768 226633 406144 674075 815101 808633 553698 822707 971520 896142 738741 918351 533243 229527 735114 977995 395993 897686 477694 359378 267154 430511 609680 262314 518548 937644 005056 724295 574134 838578 512673 408219 462506 043539 889061 160783 251095 338038 122116 634931 391461 881920 240440 726202 890365 890478 376563 057540 638205 078342 688317 272751 769274 712624 527727 511378 781684 837472 103393 573185 694867 307205 958760 026565 181772 800070 450970 840458 470008 012410 295450 556014 190509 555527 759193 434406 184345 731618 026730 812215 381727 963629 636402 043132 648032 042197 883129 119873 046875 / 899 > 25915 [i]
- extracting embedded OOA [i] would yield OOA(25915, 459, S25, 2, 898), but