Best Known (31, 31+96, s)-Nets in Base 5
(31, 31+96, 72)-Net over F5 — Constructive and digital
Digital (31, 127, 72)-net over F5, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
(31, 31+96, 293)-Net in Base 5 — Upper bound on s
There is no (31, 127, 294)-net in base 5, because
- 2 times m-reduction [i] would yield (31, 125, 294)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5125, 294, S5, 94), but
- 6 times code embedding in larger space [i] would yield OA(5131, 300, S5, 94), but
- the linear programming bound shows that M ≥ 21323 946920 157136 903964 614973 021849 598019 803499 116240 712764 365609 725187 754887 923537 585326 641109 028362 898875 271475 702561 706992 224377 002282 618774 839619 074563 959945 726919 730779 673957 907812 863271 035612 735144 150909 948137 585149 637133 018119 451967 047965 993311 626718 433256 847997 499212 596290 429116 899214 466340 247468 405781 853575 195487 810936 448563 503202 896879 149694 061455 189915 457461 712573 448942 285981 821663 627610 009227 487501 369676 704215 608444 964986 160112 904790 778231 496128 461996 013676 115469 412125 949502 875455 834126 647549 501054 155435 695676 876688 102156 861723 323798 876149 645808 644804 733221 108875 567049 841780 462925 400350 316389 812308 760595 965207 856675 562603 829329 752823 646763 277868 991425 144921 641192 984559 130763 054234 684917 385565 967873 350956 551803 392358 124256 134033 203125 / 441 305306 851747 091228 616798 416728 536783 535929 995962 466696 157009 855908 922690 309912 086922 733793 884387 490758 796788 476082 127610 069464 249075 978995 228625 386665 892769 214897 571614 054942 332558 610336 527567 390614 990478 334363 348388 335678 254134 499002 360870 730908 295794 479119 202769 518024 366270 611990 977638 269160 759589 915108 227369 324812 967757 562042 457084 571557 036143 469895 703187 324243 124059 864045 976529 732872 423857 117738 841912 904587 151208 333185 831979 817424 846963 932122 688860 686247 524485 183951 662959 947698 168485 345116 235239 610068 289593 239406 639271 271812 914708 076048 500424 769406 157695 914749 369721 950700 802073 208384 306298 039355 172858 183906 941908 839458 504004 673026 605076 096915 928641 > 5131 [i]
- 6 times code embedding in larger space [i] would yield OA(5131, 300, S5, 94), but
- extracting embedded orthogonal array [i] would yield OA(5125, 294, S5, 94), but