Best Known (35, 35+19, s)-Nets in Base 256
(35, 35+19, 14563)-Net over F256 — Constructive and digital
Digital (35, 54, 14563)-net over F256, using
- net defined by OOA [i] based on linear OOA(25654, 14563, F256, 19, 19) (dual of [(14563, 19), 276643, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25654, 131068, F256, 19) (dual of [131068, 131014, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25654, 131074, F256, 19) (dual of [131074, 131020, 20]-code), using
- (u, u+v)-construction [i] based on
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(25654, 131074, F256, 19) (dual of [131074, 131020, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25654, 131068, F256, 19) (dual of [131068, 131014, 20]-code), using
(35, 35+19, 496956)-Net over F256 — Digital
Digital (35, 54, 496956)-net over F256, using
(35, 35+19, large)-Net in Base 256 — Upper bound on s
There is no (35, 54, large)-net in base 256, because
- 17 times m-reduction [i] would yield (35, 37, large)-net in base 256, but