Best Known (13−7, 13, s)-Nets in Base 256
(13−7, 13, 21845)-Net over F256 — Constructive and digital
Digital (6, 13, 21845)-net over F256, using
- net defined by OOA [i] based on linear OOA(25613, 21845, F256, 7, 7) (dual of [(21845, 7), 152902, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25613, 21845, F256, 6, 7) (dual of [(21845, 6), 131057, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using
- an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding and stacking with additional row [i] based on linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using
- appending kth column [i] based on linear OOA(25613, 21845, F256, 6, 7) (dual of [(21845, 6), 131057, 8]-NRT-code), using
(13−7, 13, 32769)-Net over F256 — Digital
Digital (6, 13, 32769)-net over F256, using
- net defined by OOA [i] based on linear OOA(25613, 32769, F256, 7, 7) (dual of [(32769, 7), 229370, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25613, 32769, F256, 6, 7) (dual of [(32769, 6), 196601, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25613, 32769, F256, 2, 7) (dual of [(32769, 2), 65525, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [i] based on
- OOA 2-folding [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25613, 32769, F256, 2, 7) (dual of [(32769, 2), 65525, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(25613, 32769, F256, 6, 7) (dual of [(32769, 6), 196601, 8]-NRT-code), using
(13−7, 13, large)-Net in Base 256 — Upper bound on s
There is no (6, 13, large)-net in base 256, because
- 5 times m-reduction [i] would yield (6, 8, large)-net in base 256, but