Best Known (59, 59+73, s)-Nets in Base 8
(59, 59+73, 110)-Net over F8 — Constructive and digital
Digital (59, 132, 110)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (9, 45, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- digital (14, 87, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (9, 45, 45)-net over F8, using
(59, 59+73, 146)-Net over F8 — Digital
Digital (59, 132, 146)-net over F8, using
(59, 59+73, 150)-Net in Base 8
(59, 132, 150)-net in base 8, using
- base change [i] based on digital (26, 99, 150)-net over F16, using
- net from sequence [i] based on digital (26, 149)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 26 and N(F) ≥ 150, using
- net from sequence [i] based on digital (26, 149)-sequence over F16, using
(59, 59+73, 3920)-Net in Base 8 — Upper bound on s
There is no (59, 132, 3921)-net in base 8, because
- 1 times m-reduction [i] would yield (59, 131, 3921)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 20190 627584 231426 119220 826980 608207 240217 025086 538526 407855 748707 427284 452273 911535 140771 465284 177538 400250 678237 064200 > 8131 [i]