Best Known (134−26, 134, s)-Nets in Base 5
(134−26, 134, 1207)-Net over F5 — Constructive and digital
Digital (108, 134, 1207)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 6)-net over F5, using
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 0 and N(F) ≥ 6, using
- the rational function field F5(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- digital (95, 121, 1201)-net over F5, using
- net defined by OOA [i] based on linear OOA(5121, 1201, F5, 26, 26) (dual of [(1201, 26), 31105, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(5121, 15613, F5, 26) (dual of [15613, 15492, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(5121, 15613, F5, 26) (dual of [15613, 15492, 27]-code), using
- net defined by OOA [i] based on linear OOA(5121, 1201, F5, 26, 26) (dual of [(1201, 26), 31105, 27]-NRT-code), using
- digital (0, 13, 6)-net over F5, using
(134−26, 134, 15674)-Net over F5 — Digital
Digital (108, 134, 15674)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5134, 15674, F5, 26) (dual of [15674, 15540, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(513, 49, F5, 7) (dual of [49, 36, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(513, 52, F5, 7) (dual of [52, 39, 8]-code), using
- a “LX†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(513, 52, F5, 7) (dual of [52, 39, 8]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
(134−26, 134, large)-Net in Base 5 — Upper bound on s
There is no (108, 134, large)-net in base 5, because
- 24 times m-reduction [i] would yield (108, 110, large)-net in base 5, but