Best Known (34, 34+30, s)-Nets in Base 256
(34, 34+30, 4370)-Net over F256 — Constructive and digital
Digital (34, 64, 4370)-net over F256, using
- 2561 times duplication [i] based on digital (33, 63, 4370)-net over F256, using
- net defined by OOA [i] based on linear OOA(25663, 4370, F256, 30, 30) (dual of [(4370, 30), 131037, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(25663, 65550, F256, 30) (dual of [65550, 65487, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [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(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(29) ⊂ Ce(24) [i] based on
- OA 15-folding and stacking [i] based on linear OA(25663, 65550, F256, 30) (dual of [65550, 65487, 31]-code), using
- net defined by OOA [i] based on linear OOA(25663, 4370, F256, 30, 30) (dual of [(4370, 30), 131037, 31]-NRT-code), using
(34, 34+30, 18474)-Net over F256 — Digital
Digital (34, 64, 18474)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25664, 18474, F256, 3, 30) (dual of [(18474, 3), 55358, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25664, 21851, F256, 3, 30) (dual of [(21851, 3), 65489, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25664, 65553, F256, 30) (dual of [65553, 65489, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(23) [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(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to Ce(29) ⊂ Ce(23) [i] based on
- OOA 3-folding [i] based on linear OA(25664, 65553, F256, 30) (dual of [65553, 65489, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(25664, 21851, F256, 3, 30) (dual of [(21851, 3), 65489, 31]-NRT-code), using
(34, 34+30, large)-Net in Base 256 — Upper bound on s
There is no (34, 64, large)-net in base 256, because
- 28 times m-reduction [i] would yield (34, 36, large)-net in base 256, but