Best Known (65−16, 65, s)-Nets in Base 256
(65−16, 65, 1065216)-Net over F256 — Constructive and digital
Digital (49, 65, 1065216)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (11, 19, 16641)-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 (7, 15, 16384)-net over F256, using
- net defined by OOA [i] based on linear OOA(25615, 16384, F256, 8, 8) (dual of [(16384, 8), 131057, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using
- net defined by OOA [i] based on linear OOA(25615, 16384, F256, 8, 8) (dual of [(16384, 8), 131057, 9]-NRT-code), using
- 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 (11, 19, 16641)-net over F256, using
(65−16, 65, large)-Net over F256 — Digital
Digital (49, 65, large)-net over F256, using
- t-expansion [i] based on digital (47, 65, large)-net over F256, using
- 3 times m-reduction [i] based on digital (47, 68, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25668, large, F256, 21) (dual of [large, large−68, 22]-code), using
- 7 times code embedding in larger space [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]
- 7 times code embedding in larger space [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(25668, large, F256, 21) (dual of [large, large−68, 22]-code), using
- 3 times m-reduction [i] based on digital (47, 68, large)-net over F256, using
(65−16, 65, large)-Net in Base 256 — Upper bound on s
There is no (49, 65, large)-net in base 256, because
- 14 times m-reduction [i] would yield (49, 51, large)-net in base 256, but