Best Known (60−46, 60, s)-Nets in Base 5
(60−46, 60, 35)-Net over F5 — Constructive and digital
Digital (14, 60, 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]
(60−46, 60, 39)-Net over F5 — Digital
Digital (14, 60, 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
(60−46, 60, 108)-Net in Base 5 — Upper bound on s
There is no (14, 60, 109)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(560, 109, S5, 46), but
- the linear programming bound shows that M ≥ 1215 046362 954020 696308 300375 093123 767051 872630 121783 528072 027429 796749 872515 292591 837801 871239 158110 849244 592865 416036 975290 126065 374352 037906 646728 515625 / 1317 386590 649055 505351 113927 708043 525859 782568 029025 175363 079176 131194 605319 309251 279672 324235 785541 118268 547996 > 560 [i]