Best Known (17, 17+7, s)-Nets in Base 8
(17, 17+7, 520)-Net over F8 — Constructive and digital
Digital (17, 24, 520)-net over F8, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 65)-net over F8, using
- s-reduction based on digital (0, 0, s)-net over F8 with arbitrarily large s, using
- digital (0, 1, 65)-net over F8, using
- s-reduction based on digital (0, 1, s)-net over F8 with arbitrarily large s, using
- digital (0, 1, 65)-net over F8 (see above)
- digital (0, 1, 65)-net over F8 (see above)
- digital (0, 1, 65)-net over F8 (see above)
- digital (1, 3, 65)-net over F8, using
- s-reduction based on digital (1, 3, 73)-net over F8, using
- digital (1, 4, 65)-net over F8, using
- net defined by OOA [i] based on linear OOA(84, 65, F8, 3, 3) (dual of [(65, 3), 191, 4]-NRT-code), using
- digital (6, 13, 65)-net over F8, using
- base reduction for projective spaces (embedding PG(6,64) in PG(12,8)) for nets [i] based on digital (0, 7, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- base reduction for projective spaces (embedding PG(6,64) in PG(12,8)) for nets [i] based on digital (0, 7, 65)-net over F64, using
- digital (0, 0, 65)-net over F8, using
(17, 17+7, 771)-Net in Base 8 — Constructive
(17, 24, 771)-net in base 8, using
- base change [i] based on digital (11, 18, 771)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 257)-net over F16, using
- net defined by OOA [i] based on linear OOA(164, 257, F16, 3, 3) (dual of [(257, 3), 767, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(164, 257, F16, 2, 3) (dual of [(257, 2), 510, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(164, 257, F16, 3, 3) (dual of [(257, 3), 767, 4]-NRT-code), using
- digital (7, 14, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 7, 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, 7, 257)-net over F256, using
- digital (1, 4, 257)-net over F16, using
- (u, u+v)-construction [i] based on
(17, 17+7, 1755)-Net over F8 — Digital
Digital (17, 24, 1755)-net over F8, using
(17, 17+7, 2177586)-Net in Base 8 — Upper bound on s
There is no (17, 24, 2177587)-net in base 8, because
- 1 times m-reduction [i] would yield (17, 23, 2177587)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 590 296583 860536 439496 > 823 [i]