Best Known (31−16, 31, s)-Nets in Base 256
(31−16, 31, 8192)-Net over F256 — Constructive and digital
Digital (15, 31, 8192)-net over F256, using
- net defined by OOA [i] based on linear OOA(25631, 8192, F256, 16, 16) (dual of [(8192, 16), 131041, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on 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]
- OA 8-folding and stacking [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
(31−16, 31, 15685)-Net over F256 — Digital
Digital (15, 31, 15685)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25631, 15685, F256, 4, 16) (dual of [(15685, 4), 62709, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25631, 16384, F256, 4, 16) (dual of [(16384, 4), 65505, 17]-NRT-code), using
- OOA 4-folding [i] based on 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]
- OOA 4-folding [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(25631, 16384, F256, 4, 16) (dual of [(16384, 4), 65505, 17]-NRT-code), using
(31−16, 31, large)-Net in Base 256 — Upper bound on s
There is no (15, 31, large)-net in base 256, because
- 14 times m-reduction [i] would yield (15, 17, large)-net in base 256, but