Best Known (67−23, 67, s)-Nets in Base 256
(67−23, 67, 762600)-Net over F256 — Constructive and digital
Digital (44, 67, 762600)-net over F256, using
- net defined by OOA [i] based on linear OOA(25667, 762600, F256, 23, 23) (dual of [(762600, 23), 17539733, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25667, 8388601, F256, 23) (dual of [8388601, 8388534, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25667, large, F256, 23) (dual of [large, large−67, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(25667, large, F256, 23) (dual of [large, large−67, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25667, 8388601, F256, 23) (dual of [8388601, 8388534, 24]-code), using
(67−23, 67, 2796201)-Net over F256 — Digital
Digital (44, 67, 2796201)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25667, 2796201, F256, 3, 23) (dual of [(2796201, 3), 8388536, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25667, large, F256, 23) (dual of [large, large−67, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- OOA 3-folding [i] based on linear OA(25667, large, F256, 23) (dual of [large, large−67, 24]-code), using
(67−23, 67, large)-Net in Base 256 — Upper bound on s
There is no (44, 67, large)-net in base 256, because
- 21 times m-reduction [i] would yield (44, 46, large)-net in base 256, but