Best Known (5, 5+13, s)-Nets in Base 32
(5, 5+13, 76)-Net over F32 — Constructive and digital
Digital (5, 18, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
(5, 5+13, 80)-Net in Base 32 — Constructive
(5, 18, 80)-net in base 32, using
- 6 times m-reduction [i] based on (5, 24, 80)-net in base 32, using
- base change [i] based on digital (1, 20, 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
- base change [i] based on digital (1, 20, 80)-net over F64, using
(5, 5+13, 83)-Net over F32 — Digital
Digital (5, 18, 83)-net over F32, using
- net from sequence [i] based on digital (5, 82)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 83, using
(5, 5+13, 97)-Net in Base 32
(5, 18, 97)-net in base 32, using
- base change [i] based on digital (2, 15, 97)-net over F64, using
- net from sequence [i] based on digital (2, 96)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 2 and N(F) ≥ 97, using
- net from sequence [i] based on digital (2, 96)-sequence over F64, using
(5, 5+13, 1773)-Net in Base 32 — Upper bound on s
There is no (5, 18, 1774)-net in base 32, because
- 1 times m-reduction [i] would yield (5, 17, 1774)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 38 771374 948186 121018 459140 > 3217 [i]