Best Known (42, 42+16, s)-Nets in Base 256
(42, 42+16, 1049089)-Net over F256 — Constructive and digital
Digital (42, 58, 1049089)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 514)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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
- digital (0, 8, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- digital (0, 4, 257)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (30, 46, 1048575)-net over F256, using
- net defined by OOA [i] based on linear OOA(25646, 1048575, F256, 16, 16) (dual of [(1048575, 16), 16777154, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(25646, 8388600, F256, 16) (dual of [8388600, 8388554, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(25646, 8388600, F256, 16) (dual of [8388600, 8388554, 17]-code), using
- net defined by OOA [i] based on linear OOA(25646, 1048575, F256, 16, 16) (dual of [(1048575, 16), 16777154, 17]-NRT-code), using
- digital (4, 12, 514)-net over F256, using
(42, 42+16, large)-Net over F256 — Digital
Digital (42, 58, large)-net over F256, using
- 3 times m-reduction [i] based on digital (42, 61, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25661, large, F256, 19) (dual of [large, large−61, 20]-code), using
- strength reduction [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- strength reduction [i] based on linear OA(25661, large, F256, 21) (dual of [large, large−61, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25661, large, F256, 19) (dual of [large, large−61, 20]-code), using
(42, 42+16, large)-Net in Base 256 — Upper bound on s
There is no (42, 58, large)-net in base 256, because
- 14 times m-reduction [i] would yield (42, 44, large)-net in base 256, but