Best Known (79, ∞, s)-Nets in Base 5
(79, ∞, 82)-Net over F5 — Constructive and digital
Digital (79, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (79, 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
(79, ∞, 150)-Net over F5 — Digital
Digital (79, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (79, 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
(79, ∞, 334)-Net in Base 5 — Upper bound on s
There is no (79, m, 335)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (79, 1335, 335)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51335, 335, S5, 4, 1256), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 566767 445289 283878 262921 960982 793467 393863 429241 680413 281782 373695 639548 175072 489785 086348 531845 548504 188672 234907 499743 001291 726197 302831 264879 696821 638846 522637 261900 606746 444134 794286 771187 385342 134995 201471 832495 457916 907642 265730 301495 133060 252860 016275 713279 239802 653708 744636 125829 675246 120543 036186 800663 033226 034993 409582 342114 417626 725270 539872 052260 608452 956773 727981 237341 079082 154926 345499 867336 415132 598825 413547 265712 874313 027829 028612 495328 142143 939824 323126 523604 965305 401663 343355 404704 533499 209199 029925 802829 806583 025859 144257 809053 413858 318615 949046 922439 085302 839898 918546 602863 711563 715237 366751 429704 716220 918912 761018 047738 389055 046584 711499 478966 489287 579028 486805 535073 193046 752713 538645 655989 182470 560546 389719 904509 676623 710341 938693 717386 396441 609615 873608 105819 275185 620796 750518 171572 311316 038477 598001 326239 290938 417524 995675 387116 827825 523467 352156 602536 099165 058625 093394 084615 283645 689487 457275 390625 / 1257 > 51335 [i]
- extracting embedded OOA [i] would yield OOA(51335, 335, S5, 4, 1256), but