Best Known (59−30, 59, s)-Nets in Base 256
(59−30, 59, 4369)-Net over F256 — Constructive and digital
Digital (29, 59, 4369)-net over F256, using
- net defined by OOA [i] based on linear OOA(25659, 4369, F256, 30, 30) (dual of [(4369, 30), 131011, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(25659, 65535, F256, 30) (dual of [65535, 65476, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(25659, 65535, F256, 30) (dual of [65535, 65476, 31]-code), using
(59−30, 59, 10923)-Net over F256 — Digital
Digital (29, 59, 10923)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25659, 10923, F256, 6, 30) (dual of [(10923, 6), 65479, 31]-NRT-code), using
- OOA 6-folding [i] based on linear OA(25659, 65538, F256, 30) (dual of [65538, 65479, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(25659, 65536, F256, 30) (dual of [65536, 65477, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- OOA 6-folding [i] based on linear OA(25659, 65538, F256, 30) (dual of [65538, 65479, 31]-code), using
(59−30, 59, large)-Net in Base 256 — Upper bound on s
There is no (29, 59, large)-net in base 256, because
- 28 times m-reduction [i] would yield (29, 31, large)-net in base 256, but