Best Known (47, 47+17, s)-Nets in Base 256
(47, 47+17, 1064959)-Net over F256 — Constructive and digital
Digital (47, 64, 1064959)-net over F256, using
- (u, u+v)-construction [i] based on
- 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 (32, 49, 1048575)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 1048575, F256, 17, 17) (dual of [(1048575, 17), 17825726, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25649, 8388601, F256, 17) (dual of [8388601, 8388552, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(25649, large, F256, 17) (dual of [large, large−49, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(25649, large, F256, 17) (dual of [large, large−49, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25649, 8388601, F256, 17) (dual of [8388601, 8388552, 18]-code), using
- net defined by OOA [i] based on linear OOA(25649, 1048575, F256, 17, 17) (dual of [(1048575, 17), 17825726, 18]-NRT-code), using
- digital (7, 15, 16384)-net over F256, using
(47, 47+17, large)-Net over F256 — Digital
Digital (47, 64, large)-net over F256, using
- 4 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
(47, 47+17, large)-Net in Base 256 — Upper bound on s
There is no (47, 64, large)-net in base 256, because
- 15 times m-reduction [i] would yield (47, 49, large)-net in base 256, but