Best Known (121, 141, s)-Nets in Base 5
(121, 141, 39078)-Net over F5 — Constructive and digital
Digital (121, 141, 39078)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 16)-net over F5, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 3 and N(F) ≥ 16, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- digital (108, 128, 39062)-net over F5, using
- net defined by OOA [i] based on linear OOA(5128, 39062, F5, 20, 20) (dual of [(39062, 20), 781112, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(5128, 390620, F5, 20) (dual of [390620, 390492, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5128, 390625, F5, 20) (dual of [390625, 390497, 21]-code), using
- 1 times truncation [i] based on linear OA(5129, 390626, F5, 21) (dual of [390626, 390497, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(5129, 390626, F5, 21) (dual of [390626, 390497, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(5128, 390625, F5, 20) (dual of [390625, 390497, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(5128, 390620, F5, 20) (dual of [390620, 390492, 21]-code), using
- net defined by OOA [i] based on linear OOA(5128, 39062, F5, 20, 20) (dual of [(39062, 20), 781112, 21]-NRT-code), using
- digital (3, 13, 16)-net over F5, using
(121, 141, 390686)-Net over F5 — Digital
Digital (121, 141, 390686)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5141, 390686, F5, 20) (dual of [390686, 390545, 21]-code), using
- construction X applied to C([0,10]) ⊂ C([0,6]) [i] based on
- linear OA(5129, 390626, F5, 21) (dual of [390626, 390497, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(581, 390626, F5, 13) (dual of [390626, 390545, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(512, 60, F5, 6) (dual of [60, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- construction X applied to C([0,10]) ⊂ C([0,6]) [i] based on
(121, 141, large)-Net in Base 5 — Upper bound on s
There is no (121, 141, large)-net in base 5, because
- 18 times m-reduction [i] would yield (121, 123, large)-net in base 5, but