Best Known (24, 49, s)-Nets in Base 256
(24, 49, 5461)-Net over F256 — Constructive and digital
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
(24, 49, 11731)-Net over F256 — Digital
Digital (24, 49, 11731)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25649, 11731, F256, 5, 25) (dual of [(11731, 5), 58606, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25649, 13107, F256, 5, 25) (dual of [(13107, 5), 65486, 26]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25649, 65535, F256, 25) (dual of [65535, 65486, 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 5-folding [i] based on linear OA(25649, 65535, F256, 25) (dual of [65535, 65486, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(25649, 13107, F256, 5, 25) (dual of [(13107, 5), 65486, 26]-NRT-code), using
(24, 49, large)-Net in Base 256 — Upper bound on s
There is no (24, 49, large)-net in base 256, because
- 23 times m-reduction [i] would yield (24, 26, large)-net in base 256, but