Best Known (128−20, 128, s)-Nets in Base 5
(128−20, 128, 39062)-Net over F5 — Constructive and digital
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
(128−20, 128, 195312)-Net over F5 — Digital
Digital (108, 128, 195312)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5128, 195312, F5, 2, 20) (dual of [(195312, 2), 390496, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5128, 390624, F5, 20) (dual of [390624, 390496, 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
- OOA 2-folding [i] based on linear OA(5128, 390624, F5, 20) (dual of [390624, 390496, 21]-code), using
(128−20, 128, large)-Net in Base 5 — Upper bound on s
There is no (108, 128, large)-net in base 5, because
- 18 times m-reduction [i] would yield (108, 110, large)-net in base 5, but