Best Known (97−84, 97, s)-Nets in Base 25
(97−84, 97, 126)-Net over F25 — Constructive and digital
Digital (13, 97, 126)-net over F25, using
- t-expansion [i] based on digital (10, 97, 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
(97−84, 97, 1140)-Net over F25 — Upper bound on s (digital)
There is no digital (13, 97, 1141)-net over F25, because
- extracting embedded orthogonal array [i] would yield linear OA(2597, 1141, F25, 84) (dual of [1141, 1044, 85]-code), but
- the Johnson bound shows that N ≤ 28 082404 019461 397582 170062 875028 399874 194748 617977 554104 455840 268875 950641 813017 989157 774058 191163 798221 916775 989031 969227 531485 567251 521962 306349 649145 998020 166766 641719 444602 181926 478444 876217 223529 454238 982455 199251 205363 097483 207281 820782 523061 441454 868279 638165 368085 399408 505874 887153 915673 969738 259090 578834 649643 667720 444604 496772 716582 014780 135922 341396 492625 825172 450864 051808 805068 832406 567869 316951 010612 997566 638305 161486 474268 448793 243774 758493 326906 991036 264231 603761 626681 565557 646571 960179 235027 493934 592421 959503 201394 198338 828134 018555 760788 406595 298735 173603 128566 482746 769198 273991 224553 122370 847707 072598 664103 883251 629155 417988 412757 342912 632763 456457 030607 574859 179926 301073 493175 032747 191350 660073 315726 374422 411738 945182 680298 679714 665375 779350 418509 722087 068171 655762 113936 583393 482379 426627 913170 269909 372716 047611 834777 230208 755109 470985 919786 916722 867437 998813 486602 915096 941172 115894 527760 105113 634514 586635 446325 132031 852509 580773 552417 924855 742457 272087 920238 770545 943162 621772 735217 608827 333955 469476 627645 044370 595371 438402 612316 669265 410606 646588 243298 079469 665107 591577 930226 381442 647900 132250 164522 055308 720654 434855 499404 122986 694939 438844 321683 357655 532322 767951 668041 374929 499672 759333 751715 467395 555776 066947 177790 670589 581267 031000 428367 928595 547428 882482 330613 842250 732888 492454 411173 736258 669596 527146 743401 843472 072548 247154 697965 995282 966076 916146 003693 072773 916189 985293 258779 025259 139940 264142 014125 739581 152500 < 251044 [i]
(97−84, 97, 1142)-Net in Base 25 — Upper bound on s
There is no (13, 97, 1143)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 4067 370442 355815 231268 623773 524076 926066 320775 941581 818799 696614 734718 034101 860937 712308 138368 839067 709307 592215 726532 663025 000912 236945 > 2597 [i]