Best Known (109−107, 109, s)-Nets in Base 32
(109−107, 109, 44)-Net over F32 — Constructive and digital
Digital (2, 109, 44)-net over F32, using
- t-expansion [i] based on digital (1, 109, 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
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
(109−107, 109, 53)-Net over F32 — Digital
Digital (2, 109, 53)-net over F32, using
- net from sequence [i] based on digital (2, 52)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 2 and N(F) ≥ 53, using
(109−107, 109, 90)-Net in Base 32 — Upper bound on s
There is no (2, 109, 91)-net in base 32, because
- 22 times m-reduction [i] would yield (2, 87, 91)-net in base 32, but
- extracting embedded orthogonal array [i] would yield OA(3287, 91, S32, 85), but
- the linear programming bound shows that M ≥ 3218 248804 644806 290772 103657 191613 826913 486259 137011 802066 676331 137713 410455 220883 164990 453062 699224 855954 368127 744971 436177 620882 948096 / 34443 > 3287 [i]
- extracting embedded orthogonal array [i] would yield OA(3287, 91, S32, 85), but