Best Known (32−31, 32, s)-Nets in Base 32
(32−31, 32, 44)-Net over F32 — Constructive and digital
Digital (1, 32, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
(32−31, 32, 165)-Net in Base 32 — Upper bound on s
There is no (1, 32, 166)-net in base 32, because
- 23 times m-reduction [i] would yield (1, 9, 166)-net in base 32, but
- extracting embedded orthogonal array [i] would yield OA(329, 166, S32, 8), but
- the linear programming bound shows that M ≥ 2 187320 464516 698429 456384 / 61939 225499 > 329 [i]
- extracting embedded orthogonal array [i] would yield OA(329, 166, S32, 8), but