Best Known (70−45, 70, s)-Nets in Base 32
(70−45, 70, 120)-Net over F32 — Constructive and digital
Digital (25, 70, 120)-net over F32, using
- t-expansion [i] based on digital (11, 70, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(70−45, 70, 216)-Net in Base 32 — Constructive
(25, 70, 216)-net in base 32, using
- base change [i] based on digital (5, 50, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(70−45, 70, 225)-Net over F32 — Digital
Digital (25, 70, 225)-net over F32, using
- t-expansion [i] based on digital (24, 70, 225)-net over F32, using
- net from sequence [i] based on digital (24, 224)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 24 and N(F) ≥ 225, using
- net from sequence [i] based on digital (24, 224)-sequence over F32, using
(70−45, 70, 257)-Net in Base 32
(25, 70, 257)-net in base 32, using
- 8 times m-reduction [i] based on (25, 78, 257)-net in base 32, using
- base change [i] based on digital (12, 65, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- base change [i] based on digital (12, 65, 257)-net over F64, using
(70−45, 70, 15341)-Net in Base 32 — Upper bound on s
There is no (25, 70, 15342)-net in base 32, because
- 1 times m-reduction [i] would yield (25, 69, 15342)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 71 708647 009672 997483 211659 777115 782686 098986 832277 144029 620377 442336 891919 989876 828623 592960 135131 609896 > 3269 [i]