Best Known (29, 40, s)-Nets in Base 256
(29, 40, 1710617)-Net over F256 — Constructive and digital
Digital (29, 40, 1710617)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (4, 9, 32897)-net over F256, using
- net defined by OOA [i] based on linear OOA(2569, 32897, F256, 5, 5) (dual of [(32897, 5), 164476, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(2569, 32897, F256, 4, 5) (dual of [(32897, 4), 131579, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2562, 257, F256, 4, 2) (dual of [(257, 4), 1026, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;1026,256) [i]
- linear OOA(2567, 32640, F256, 4, 5) (dual of [(32640, 4), 130553, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- linear OOA(2562, 257, F256, 4, 2) (dual of [(257, 4), 1026, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2569, 32897, F256, 4, 5) (dual of [(32897, 4), 131579, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2569, 32897, F256, 5, 5) (dual of [(32897, 5), 164476, 6]-NRT-code), using
- digital (20, 31, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- digital (4, 9, 32897)-net over F256, using
(29, 40, large)-Net over F256 — Digital
Digital (29, 40, large)-net over F256, using
- t-expansion [i] based on digital (28, 40, large)-net over F256, using
- 1 times m-reduction [i] based on digital (28, 41, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25641, large, F256, 13) (dual of [large, large−41, 14]-code), using
- 4 times code embedding in larger space [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 4 times code embedding in larger space [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25641, large, F256, 13) (dual of [large, large−41, 14]-code), using
- 1 times m-reduction [i] based on digital (28, 41, large)-net over F256, using
(29, 40, large)-Net in Base 256 — Upper bound on s
There is no (29, 40, large)-net in base 256, because
- 9 times m-reduction [i] would yield (29, 31, large)-net in base 256, but