Best Known (16, 16+47, s)-Nets in Base 5
(16, 16+47, 37)-Net over F5 — Constructive and digital
Digital (16, 63, 37)-net over F5, using
- net from sequence [i] based on digital (16, 36)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 5 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(16, 16+47, 40)-Net over F5 — Digital
Digital (16, 63, 40)-net over F5, using
- net from sequence [i] based on digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(16, 16+47, 142)-Net in Base 5 — Upper bound on s
There is no (16, 63, 143)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(563, 143, S5, 47), but
- the linear programming bound shows that M ≥ 276527 437307 223370 123455 631602 041943 333899 701666 568631 460594 405236 557738 389029 605210 893999 554832 184801 116971 029869 774289 895566 889228 879884 454759 263689 993531 443178 653717 041015 625000 / 2410 382110 020903 259815 040486 738158 785560 284325 920123 424815 227264 999413 434481 418741 779121 861867 484897 650087 544210 925725 971547 527620 654049 > 563 [i]