Best Known (57−43, 57, s)-Nets in Base 5
(57−43, 57, 35)-Net over F5 — Constructive and digital
Digital (14, 57, 35)-net over F5, using
- net from sequence [i] based on digital (14, 34)-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 3 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]
(57−43, 57, 39)-Net over F5 — Digital
Digital (14, 57, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
(57−43, 57, 124)-Net in Base 5 — Upper bound on s
There is no (14, 57, 125)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(557, 125, S5, 43), but
- the linear programming bound shows that M ≥ 17961 856003 588537 355822 110963 679100 633458 267622 718835 518832 785126 715138 708035 468022 798269 044252 873186 112606 135323 575564 492235 361744 482141 308571 154780 793222 016654 908657 073974 609375 / 2 293145 170915 434711 346702 443683 486227 988420 723748 170622 542330 655319 861837 475276 446572 458160 916408 961366 817563 353006 208712 550662 736623 652601 > 557 [i]