Best Known (43, 43+23, s)-Nets in Base 256
(43, 43+23, 11915)-Net over F256 — Constructive and digital
Digital (43, 66, 11915)-net over F256, using
- net defined by OOA [i] based on linear OOA(25666, 11915, F256, 23, 23) (dual of [(11915, 23), 273979, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25666, 131066, F256, 23) (dual of [131066, 131000, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25666, 131074, F256, 23) (dual of [131074, 131008, 24]-code), using
- (u, u+v)-construction [i] based on
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(25666, 131074, F256, 23) (dual of [131074, 131008, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25666, 131066, F256, 23) (dual of [131066, 131000, 24]-code), using
(43, 43+23, 595718)-Net over F256 — Digital
Digital (43, 66, 595718)-net over F256, using
(43, 43+23, large)-Net in Base 256 — Upper bound on s
There is no (43, 66, large)-net in base 256, because
- 21 times m-reduction [i] would yield (43, 45, large)-net in base 256, but