Best Known (36, 36+15, s)-Nets in Base 8
(36, 36+15, 363)-Net over F8 — Constructive and digital
Digital (36, 51, 363)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (29, 44, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 22, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 22, 177)-net over F64, using
- digital (0, 7, 9)-net over F8, using
(36, 36+15, 539)-Net in Base 8 — Constructive
(36, 51, 539)-net in base 8, using
- (u, u+v)-construction [i] based on
- digital (4, 11, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- (25, 40, 514)-net in base 8, using
- base change [i] based on digital (15, 30, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 15, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 15, 257)-net over F256, using
- base change [i] based on digital (15, 30, 514)-net over F16, using
- digital (4, 11, 25)-net over F8, using
(36, 36+15, 1690)-Net over F8 — Digital
Digital (36, 51, 1690)-net over F8, using
(36, 36+15, 1362894)-Net in Base 8 — Upper bound on s
There is no (36, 51, 1362895)-net in base 8, because
- 1 times m-reduction [i] would yield (36, 50, 1362895)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1427 254607 894837 795622 881878 816597 563284 211584 > 850 [i]