Best Known (3, 3+9, s)-Nets in Base 32
(3, 3+9, 64)-Net over F32 — Constructive and digital
Digital (3, 12, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
(3, 3+9, 80)-Net in Base 32 — Constructive
(3, 12, 80)-net in base 32, using
- base change [i] based on digital (1, 10, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(3, 3+9, 81)-Net in Base 32
(3, 12, 81)-net in base 32, using
- base change [i] based on digital (1, 10, 81)-net over F64, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 81, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
(3, 3+9, 982)-Net in Base 32 — Upper bound on s
There is no (3, 12, 983)-net in base 32, because
- 1 times m-reduction [i] would yield (3, 11, 983)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 36168 009159 547779 > 3211 [i]