Best Known (23, 23+13, s)-Nets in Base 256
(23, 23+13, 21845)-Net over F256 — Constructive and digital
Digital (23, 36, 21845)-net over F256, using
- net defined by OOA [i] based on linear OOA(25636, 21845, F256, 13, 13) (dual of [(21845, 13), 283949, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25636, 131071, F256, 13) (dual of [131071, 131035, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(25636, 131073, F256, 13) (dual of [131073, 131037, 14]-code), using
- (u, u+v)-construction [i] based on
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(25636, 131073, F256, 13) (dual of [131073, 131037, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(25636, 131071, F256, 13) (dual of [131071, 131035, 14]-code), using
(23, 23+13, 347975)-Net over F256 — Digital
Digital (23, 36, 347975)-net over F256, using
(23, 23+13, large)-Net in Base 256 — Upper bound on s
There is no (23, 36, large)-net in base 256, because
- 11 times m-reduction [i] would yield (23, 25, large)-net in base 256, but