Best Known (28−11, 28, s)-Nets in Base 8
(28−11, 28, 208)-Net over F8 — Constructive and digital
Digital (17, 28, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 14, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
(28−11, 28, 299)-Net over F8 — Digital
Digital (17, 28, 299)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(828, 299, F8, 11) (dual of [299, 271, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(828, 511, F8, 11) (dual of [511, 483, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(828, 511, F8, 11) (dual of [511, 483, 12]-code), using
(28−11, 28, 300)-Net in Base 8 — Constructive
(17, 28, 300)-net in base 8, using
- trace code for nets [i] based on (3, 14, 150)-net in base 64, using
- base change [i] based on digital (1, 12, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 12, 150)-net over F128, using
(28−11, 28, 28014)-Net in Base 8 — Upper bound on s
There is no (17, 28, 28015)-net in base 8, because
- 1 times m-reduction [i] would yield (17, 27, 28015)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 2 418089 981660 167929 408022 > 827 [i]