Best Known (61−49, 61, s)-Nets in Base 5
(61−49, 61, 33)-Net over F5 — Constructive and digital
Digital (12, 61, 33)-net over F5, using
- net from sequence [i] based on digital (12, 32)-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 1 place 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]
(61−49, 61, 69)-Net in Base 5 — Upper bound on s
There is no (12, 61, 70)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(561, 70, S5, 49), but
- the linear programming bound shows that M ≥ 191361 683443 691532 602315 419353 544712 066650 390625 / 35929 > 561 [i]