Best Known (27, 27+15, s)-Nets in Base 256
(27, 27+15, 18725)-Net over F256 — Constructive and digital
Digital (27, 42, 18725)-net over F256, using
- net defined by OOA [i] based on linear OOA(25642, 18725, F256, 15, 15) (dual of [(18725, 15), 280833, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25642, 131076, F256, 15) (dual of [131076, 131034, 16]-code), using
- (u, u+v)-construction [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
- linear OA(25629, 65538, F256, 15) (dual of [65538, 65509, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(25629, 65536, F256, 15) (dual of [65536, 65507, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code) (see above)
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- (u, u+v)-construction [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(25642, 131076, F256, 15) (dual of [131076, 131034, 16]-code), using
(27, 27+15, 397782)-Net over F256 — Digital
Digital (27, 42, 397782)-net over F256, using
(27, 27+15, large)-Net in Base 256 — Upper bound on s
There is no (27, 42, large)-net in base 256, because
- 13 times m-reduction [i] would yield (27, 29, large)-net in base 256, but