Best Known (77, 77+∞, s)-Nets in Base 5
(77, 77+∞, 82)-Net over F5 — Constructive and digital
Digital (77, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (77, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(77, 77+∞, 150)-Net over F5 — Digital
Digital (77, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (77, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
(77, 77+∞, 326)-Net in Base 5 — Upper bound on s
There is no (77, m, 327)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (77, 1303, 327)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51303, 327, S5, 4, 1226), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 36 938169 043641 239314 688547 257790 802311 483170 534523 691992 510220 604206 517005 737239 339253 375368 232808 250648 797312 931798 217833 510257 600537 440814 964195 710332 729476 129554 724568 778400 803986 934794 304324 361352 112342 902845 721056 635194 661728 802791 928717 878317 068094 352928 776537 392597 141644 836375 519110 620525 769203 496872 417867 616832 094434 948036 060251 050088 217024 892723 427906 477571 736472 690190 453717 396792 765159 891900 877421 017390 818134 141732 322720 135890 365610 951541 426602 096240 759798 382233 102353 279046 208018 448806 212786 889712 809188 799203 274062 667405 846831 515552 957245 097552 817679 567250 101757 045992 022317 129982 911754 514373 041076 685003 032110 308692 185972 404207 679287 715854 916255 504351 106217 983551 717619 772737 562181 758913 521505 728789 575952 588988 768566 482965 818195 849814 388014 744753 536479 113538 922740 704902 276307 635140 723871 262885 239387 699381 702899 256486 200518 108606 350185 989864 791006 754966 319614 030823 004213 743843 138217 926025 390625 / 409 > 51303 [i]
- extracting embedded OOA [i] would yield OOA(51303, 327, S5, 4, 1226), but