Best Known (15, 56, s)-Nets in Base 5
(15, 56, 36)-Net over F5 — Constructive and digital
Digital (15, 56, 36)-net over F5, using
- net from sequence [i] based on digital (15, 35)-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 4 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]
(15, 56, 39)-Net over F5 — Digital
Digital (15, 56, 39)-net over F5, using
- t-expansion [i] based on digital (14, 56, 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
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
(15, 56, 148)-Net in Base 5 — Upper bound on s
There is no (15, 56, 149)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(556, 149, S5, 41), but
- the linear programming bound shows that M ≥ 572 078975 469705 953424 623342 004460 721768 116576 630226 648774 807156 675041 078236 443513 596896 082162 857055 664062 500000 000000 / 388673 139085 638175 334731 197626 662833 952575 177980 704147 964287 113139 126680 294113 > 556 [i]