Best Known (37, 62, s)-Nets in Base 256
(37, 62, 5719)-Net over F256 — Constructive and digital
Digital (37, 62, 5719)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (24, 49, 5461)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 5461, F256, 25, 25) (dual of [(5461, 25), 136476, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25649, 65533, F256, 25) (dual of [65533, 65484, 26]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(25649, 65533, F256, 25) (dual of [65533, 65484, 26]-code), using
- net defined by OOA [i] based on linear OOA(25649, 5461, F256, 25, 25) (dual of [(5461, 25), 136476, 26]-NRT-code), using
- digital (1, 13, 258)-net over F256, using
(37, 62, 65827)-Net over F256 — Digital
Digital (37, 62, 65827)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25662, 65827, F256, 25) (dual of [65827, 65765, 26]-code), using
- (u, u+v)-construction [i] based on
- linear OA(25613, 289, F256, 12) (dual of [289, 276, 13]-code), using
- extended algebraic-geometric code AGe(F,276P) [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- linear OA(25649, 65538, F256, 25) (dual of [65538, 65489, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- 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(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(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(24) ⊂ Ce(23) [i] based on
- linear OA(25613, 289, F256, 12) (dual of [289, 276, 13]-code), using
- (u, u+v)-construction [i] based on
(37, 62, large)-Net in Base 256 — Upper bound on s
There is no (37, 62, large)-net in base 256, because
- 23 times m-reduction [i] would yield (37, 39, large)-net in base 256, but