Best Known (24−14, 24, s)-Nets in Base 256
(24−14, 24, 517)-Net over F256 — Constructive and digital
Digital (10, 24, 517)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (2, 16, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (1, 8, 258)-net over F256, using
(24−14, 24, 777)-Net over F256 — Digital
Digital (10, 24, 777)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25624, 777, F256, 14) (dual of [777, 753, 15]-code), using
- 3 step Varšamov–Edel lengthening with (ri) = (1, 0, 0) [i] based on linear OA(25623, 773, F256, 14) (dual of [773, 750, 15]-code), using
- construction X applied to C([250,263]) ⊂ C([251,263]) [i] based on
- linear OA(25623, 771, F256, 14) (dual of [771, 748, 15]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {250,251,…,263}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(25621, 771, F256, 13) (dual of [771, 750, 14]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {251,252,…,263}, and designed minimum distance d ≥ |I|+1 = 14 [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 C([250,263]) ⊂ C([251,263]) [i] based on
- 3 step Varšamov–Edel lengthening with (ri) = (1, 0, 0) [i] based on linear OA(25623, 773, F256, 14) (dual of [773, 750, 15]-code), using
(24−14, 24, 2394421)-Net in Base 256 — Upper bound on s
There is no (10, 24, 2394422)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 6277 105522 047008 781596 424007 944320 111096 381844 870002 851096 > 25624 [i]