Best Known (43, 65, s)-Nets in Base 256
(43, 65, 762600)-Net over F256 — Constructive and digital
Digital (43, 65, 762600)-net over F256, using
- 2561 times duplication [i] based on digital (42, 64, 762600)-net over F256, using
- net defined by OOA [i] based on linear OOA(25664, 762600, F256, 22, 22) (dual of [(762600, 22), 16777136, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(25664, 8388600, F256, 22) (dual of [8388600, 8388536, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(25664, 8388600, F256, 22) (dual of [8388600, 8388536, 23]-code), using
- net defined by OOA [i] based on linear OOA(25664, 762600, F256, 22, 22) (dual of [(762600, 22), 16777136, 23]-NRT-code), using
(43, 65, 3005321)-Net over F256 — Digital
Digital (43, 65, 3005321)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25665, 3005321, F256, 2, 22) (dual of [(3005321, 2), 6010577, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25665, 4194301, F256, 2, 22) (dual of [(4194301, 2), 8388537, 23]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25664, 4194301, F256, 2, 22) (dual of [(4194301, 2), 8388538, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25664, 8388602, F256, 22) (dual of [8388602, 8388538, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- OOA 2-folding [i] based on linear OA(25664, 8388602, F256, 22) (dual of [8388602, 8388538, 23]-code), using
- 2561 times duplication [i] based on linear OOA(25664, 4194301, F256, 2, 22) (dual of [(4194301, 2), 8388538, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25665, 4194301, F256, 2, 22) (dual of [(4194301, 2), 8388537, 23]-NRT-code), using
(43, 65, large)-Net in Base 256 — Upper bound on s
There is no (43, 65, large)-net in base 256, because
- 20 times m-reduction [i] would yield (43, 45, large)-net in base 256, but