Best Known (63−45, 63, s)-Nets in Base 5
(63−45, 63, 43)-Net over F5 — Constructive and digital
Digital (18, 63, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
(63−45, 63, 185)-Net in Base 5 — Upper bound on s
There is no (18, 63, 186)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(563, 186, S5, 45), but
- the linear programming bound shows that M ≥ 23 499332 778254 763383 546588 950352 499689 164625 186072 177658 647493 236436 330213 250425 913429 353386 163711 547851 562500 000000 / 210985 505787 197629 832079 948372 223502 174403 621163 361920 786976 533234 503967 > 563 [i]