Best Known (94−81, 94, s)-Nets in Base 25
(94−81, 94, 126)-Net over F25 — Constructive and digital
Digital (13, 94, 126)-net over F25, using
- t-expansion [i] based on digital (10, 94, 126)-net over F25, using
- net from sequence [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
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(94−81, 94, 1146)-Net over F25 — Upper bound on s (digital)
There is no digital (13, 94, 1147)-net over F25, because
- 1 times m-reduction [i] would yield digital (13, 93, 1147)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(2593, 1147, F25, 80) (dual of [1147, 1054, 81]-code), but
- the Johnson bound shows that N ≤ 2632 177784 943442 532834 070649 586469 520385 740659 316000 800097 668897 937660 736392 755959 845786 361258 104006 071058 117556 595329 979516 197389 720097 160355 422681 361100 687410 696891 966325 820902 759495 060563 434113 624863 249404 027632 460842 559417 944374 048961 480824 596785 959714 915977 836320 886045 926099 626472 900165 499297 440299 025675 049894 576279 654856 716546 661976 280261 049346 847411 185246 725476 779974 000431 558843 267488 302870 560374 277772 811595 931757 449505 138742 192399 659881 808605 372235 002744 511766 676289 869623 772643 628735 736622 377205 852458 420398 567596 800465 017953 894928 270451 752723 094723 064900 659753 802610 232562 428214 737071 537938 327130 879881 767798 169474 391073 956382 920833 323928 081179 899669 522147 785357 221058 308376 755339 360790 539498 994852 758029 535572 918527 756924 153632 066153 391665 255280 033859 289275 134966 437340 695767 890617 990590 650148 329383 955081 955707 024502 551826 761023 376241 425048 161985 625310 411354 729834 435613 471257 270589 436412 437633 612257 502992 378781 145177 723471 676890 664104 810777 885236 846849 357232 512284 182362 076677 909403 585057 953680 503945 070825 113190 811856 127564 655448 356632 623241 829159 194571 631608 124085 242272 773424 129882 289417 673145 415168 229607 079153 826288 268086 042522 314537 355988 353135 056958 829173 176615 097408 287052 874751 111525 719530 484723 445796 733528 276700 084142 417607 950742 851662 916405 155160 015828 138202 668293 289284 343537 480580 416838 378782 295443 073067 071535 377512 010968 348807 333949 363923 365297 669332 425153 079168 692275 400169 550948 604369 578033 405872 075866 478650 771997 268384 461638 011689 520504 < 251054 [i]
- extracting embedded orthogonal array [i] would yield linear OA(2593, 1147, F25, 80) (dual of [1147, 1054, 81]-code), but
(94−81, 94, 1147)-Net in Base 25 — Upper bound on s
There is no (13, 94, 1148)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 93, 1148)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 10246 829168 581195 355053 773061 466598 111121 339525 820278 880010 215204 827582 361352 802523 097133 692600 956623 624751 496317 982634 428514 063105 > 2593 [i]