Best Known (68−16, 68, s)-Nets in Base 256
(68−16, 68, 2097150)-Net over F256 — Constructive and digital
Digital (52, 68, 2097150)-net over F256, using
- net defined by OOA [i] based on linear OOA(25668, 2097150, F256, 18, 16) (dual of [(2097150, 18), 37748632, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(25668, 8388601, F256, 2, 16) (dual of [(8388601, 2), 16777134, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25668, 8388602, F256, 2, 16) (dual of [(8388602, 2), 16777136, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(25622, 4194301, F256, 2, 8) (dual of [(4194301, 2), 8388580, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25622, 8388602, F256, 8) (dual of [8388602, 8388580, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- OOA 2-folding [i] based on linear OA(25622, 8388602, F256, 8) (dual of [8388602, 8388580, 9]-code), using
- linear OOA(25646, 4194301, F256, 2, 16) (dual of [(4194301, 2), 8388556, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 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
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 17]-code), using
- linear OOA(25622, 4194301, F256, 2, 8) (dual of [(4194301, 2), 8388580, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(25668, 8388602, F256, 2, 16) (dual of [(8388602, 2), 16777136, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(25668, 8388601, F256, 2, 16) (dual of [(8388601, 2), 16777134, 17]-NRT-code), using
(68−16, 68, large)-Net over F256 — Digital
Digital (52, 68, large)-net over F256, using
- t-expansion [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
(68−16, 68, large)-Net in Base 256 — Upper bound on s
There is no (52, 68, large)-net in base 256, because
- 14 times m-reduction [i] would yield (52, 54, large)-net in base 256, but