Best Known (18, 36, s)-Nets in Base 256
(18, 36, 7282)-Net over F256 — Constructive and digital
Digital (18, 36, 7282)-net over F256, using
- 2561 times duplication [i] based on digital (17, 35, 7282)-net over F256, using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [i] based on
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
(18, 36, 16385)-Net over F256 — Digital
Digital (18, 36, 16385)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25636, 16385, F256, 4, 18) (dual of [(16385, 4), 65504, 19]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25636, 65540, F256, 18) (dual of [65540, 65504, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(25636, 65541, F256, 18) (dual of [65541, 65505, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(17) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(25636, 65541, F256, 18) (dual of [65541, 65505, 19]-code), using
- OOA 4-folding [i] based on linear OA(25636, 65540, F256, 18) (dual of [65540, 65504, 19]-code), using
(18, 36, large)-Net in Base 256 — Upper bound on s
There is no (18, 36, large)-net in base 256, because
- 16 times m-reduction [i] would yield (18, 20, large)-net in base 256, but