Best Known (47−38, 47, s)-Nets in Base 5
(47−38, 47, 26)-Net over F5 — Constructive and digital
Digital (9, 47, 26)-net over F5, using
- net from sequence [i] based on digital (9, 25)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 9 and N(F) ≥ 26, using
(47−38, 47, 56)-Net in Base 5 — Upper bound on s
There is no (9, 47, 57)-net in base 5, because
- 1 times m-reduction [i] would yield (9, 46, 57)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(546, 57, S5, 37), but
- the linear programming bound shows that M ≥ 12824 852291 259958 292357 623577 117919 921875 / 78 608816 > 546 [i]
- extracting embedded orthogonal array [i] would yield OA(546, 57, S5, 37), but