Best Known (14, 101, s)-Nets in Base 25
(14, 101, 126)-Net over F25 — Constructive and digital
Digital (14, 101, 126)-net over F25, using
- t-expansion [i] based on digital (10, 101, 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
(14, 101, 130)-Net over F25 — Digital
Digital (14, 101, 130)-net over F25, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(14, 101, 1229)-Net over F25 — Upper bound on s (digital)
There is no digital (14, 101, 1230)-net over F25, because
- 1 times m-reduction [i] would yield digital (14, 100, 1230)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(25100, 1230, F25, 86) (dual of [1230, 1130, 87]-code), but
- the Johnson bound shows that N ≤ 46 681546 562636 385070 342890 254999 716969 227226 160456 023705 949658 402946 386431 408473 426071 361039 829988 950085 944922 086729 519194 221557 576682 887187 051271 465493 876631 462033 358262 160900 101894 227437 434738 433358 482859 333819 491307 981392 311943 677591 281350 394257 882549 415111 550240 907388 104090 146946 010252 740557 675792 288284 624022 112331 853719 639166 020134 060778 664307 232733 228971 034885 009946 627161 543310 310062 598672 002729 261077 012433 966491 812249 446087 323725 634470 118409 288504 771177 193291 180391 953682 160699 964093 649983 447026 101448 181728 982322 391817 061207 614144 511004 734920 374019 237851 394672 646698 874267 290325 054048 458967 535065 533322 806148 076278 161267 783306 928367 825422 286906 558676 966494 717337 427936 432223 195255 439058 003124 098988 202780 977366 992049 408482 017465 565808 071881 315799 243269 158714 906488 801295 170487 580424 010677 087382 253220 193261 783611 219767 622564 245753 680428 058696 980680 023975 851625 827197 016125 110619 989493 298960 255020 266297 789957 210495 632884 154471 971898 222447 982622 765086 624374 357153 124824 993742 645478 180746 666257 365749 546995 054087 284001 599426 011429 426583 786772 589397 737054 690468 663464 978990 598589 736358 249653 423829 421791 504288 523194 563086 376561 940438 832658 663675 430471 905241 196876 358241 252443 834678 194107 581487 661395 215403 131748 880600 698819 283135 010632 659671 749457 097391 182495 116540 320817 444640 493385 852488 896179 782250 309383 688058 569678 222980 286614 169499 488009 683037 826857 814090 001694 502999 394106 433007 291807 180407 994154 191972 779005 806732 636906 891626 334543 326275 596947 835094 037924 328878 739255 195955 077989 268173 892890 223814 288673 186527 807595 489294 483425 599936 330129 254435 904430 555591 123593 < 251130 [i]
- extracting embedded orthogonal array [i] would yield linear OA(25100, 1230, F25, 86) (dual of [1230, 1130, 87]-code), but
(14, 101, 1231)-Net in Base 25 — Upper bound on s
There is no (14, 101, 1232)-net in base 25, because
- 1 times m-reduction [i] would yield (14, 100, 1232)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 63 847478 613891 580158 673008 233140 447445 186371 429390 288624 684243 019284 999884 138270 711005 048360 426127 792622 790543 658878 256046 581073 381911 940225 > 25100 [i]