Best Known (18, 18+15, s)-Nets in Base 256
(18, 18+15, 9364)-Net over F256 — Constructive and digital
Digital (18, 33, 9364)-net over F256, using
- net defined by OOA [i] based on linear OOA(25633, 9364, F256, 15, 15) (dual of [(9364, 15), 140427, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25633, 65549, F256, 15) (dual of [65549, 65516, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25633, 65550, F256, 15) (dual of [65550, 65517, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [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(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(25633, 65550, F256, 15) (dual of [65550, 65517, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25633, 65549, F256, 15) (dual of [65549, 65516, 16]-code), using
(18, 18+15, 32775)-Net over F256 — Digital
Digital (18, 33, 32775)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25633, 32775, F256, 2, 15) (dual of [(32775, 2), 65517, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25633, 65550, F256, 15) (dual of [65550, 65517, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [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(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(25633, 65550, F256, 15) (dual of [65550, 65517, 16]-code), using
(18, 18+15, large)-Net in Base 256 — Upper bound on s
There is no (18, 33, large)-net in base 256, because
- 13 times m-reduction [i] would yield (18, 20, large)-net in base 256, but