Best Known (42−16, 42, s)-Nets in Base 8
(42−16, 42, 256)-Net over F8 — Constructive and digital
Digital (26, 42, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 21, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
(42−16, 42, 300)-Net in Base 8 — Constructive
(26, 42, 300)-net in base 8, using
- t-expansion [i] based on (25, 42, 300)-net in base 8, using
- trace code for nets [i] based on (4, 21, 150)-net in base 64, using
- base change [i] based on digital (1, 18, 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, 18, 150)-net over F128, using
- trace code for nets [i] based on (4, 21, 150)-net in base 64, using
(42−16, 42, 374)-Net over F8 — Digital
Digital (26, 42, 374)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(842, 374, F8, 16) (dual of [374, 332, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(842, 511, F8, 16) (dual of [511, 469, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(842, 511, F8, 16) (dual of [511, 469, 17]-code), using
(42−16, 42, 29631)-Net in Base 8 — Upper bound on s
There is no (26, 42, 29632)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 85 093389 120195 041495 483069 207457 723545 > 842 [i]