Best Known (24, 24+24, s)-Nets in Base 256
(24, 24+24, 5461)-Net over F256 — Constructive and digital
Digital (24, 48, 5461)-net over F256, using
- 1 times m-reduction [i] based on digital (24, 49, 5461)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 5461, F256, 25, 25) (dual of [(5461, 25), 136476, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25649, 65533, F256, 25) (dual of [65533, 65484, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25649, 65533, F256, 25) (dual of [65533, 65484, 26]-code), using
- net defined by OOA [i] based on linear OOA(25649, 5461, F256, 25, 25) (dual of [(5461, 25), 136476, 26]-NRT-code), using
(24, 24+24, 13108)-Net over F256 — Digital
Digital (24, 48, 13108)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25648, 13108, F256, 5, 24) (dual of [(13108, 5), 65492, 25]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25648, 65540, F256, 24) (dual of [65540, 65492, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(25648, 65541, F256, 24) (dual of [65541, 65493, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(25648, 65541, F256, 24) (dual of [65541, 65493, 25]-code), using
- OOA 5-folding [i] based on linear OA(25648, 65540, F256, 24) (dual of [65540, 65492, 25]-code), using
(24, 24+24, large)-Net in Base 256 — Upper bound on s
There is no (24, 48, large)-net in base 256, because
- 22 times m-reduction [i] would yield (24, 26, large)-net in base 256, but