Best Known (12, 12+45, s)-Nets in Base 5
(12, 12+45, 33)-Net over F5 — Constructive and digital
Digital (12, 57, 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]
(12, 12+45, 75)-Net in Base 5 — Upper bound on s
There is no (12, 57, 76)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(557, 76, S5, 45), but
- the linear programming bound shows that M ≥ 1 684797 172108 766505 349564 113203 086890 280246 734619 140625 / 176 925564 374832 > 557 [i]