Best Known (148−23, 148, s)-Nets in Base 5
(148−23, 148, 35513)-Net over F5 — Constructive and digital
Digital (125, 148, 35513)-net over F5, using
- 51 times duplication [i] based on digital (124, 147, 35513)-net over F5, using
- net defined by OOA [i] based on linear OOA(5147, 35513, F5, 23, 23) (dual of [(35513, 23), 816652, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5147, 390644, F5, 23) (dual of [390644, 390497, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5146, 390643, F5, 23) (dual of [390643, 390497, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(5145, 390626, F5, 23) (dual of [390626, 390481, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- 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(51, 17, F5, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(5146, 390643, F5, 23) (dual of [390643, 390497, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5147, 390644, F5, 23) (dual of [390644, 390497, 24]-code), using
- net defined by OOA [i] based on linear OOA(5147, 35513, F5, 23, 23) (dual of [(35513, 23), 816652, 24]-NRT-code), using
(148−23, 148, 195322)-Net over F5 — Digital
Digital (125, 148, 195322)-net over F5, using
- 51 times duplication [i] based on digital (124, 147, 195322)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5147, 195322, F5, 2, 23) (dual of [(195322, 2), 390497, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5147, 390644, F5, 23) (dual of [390644, 390497, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5146, 390643, F5, 23) (dual of [390643, 390497, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(5145, 390626, F5, 23) (dual of [390626, 390481, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 516−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- 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(51, 17, F5, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(5146, 390643, F5, 23) (dual of [390643, 390497, 24]-code), using
- OOA 2-folding [i] based on linear OA(5147, 390644, F5, 23) (dual of [390644, 390497, 24]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5147, 195322, F5, 2, 23) (dual of [(195322, 2), 390497, 24]-NRT-code), using
(148−23, 148, large)-Net in Base 5 — Upper bound on s
There is no (125, 148, large)-net in base 5, because
- 21 times m-reduction [i] would yield (125, 127, large)-net in base 5, but