Best Known (112, 112+20, s)-Nets in Base 5
(112, 112+20, 39065)-Net over F5 — Constructive and digital
Digital (112, 132, 39065)-net over F5, using
- net defined by OOA [i] based on linear OOA(5132, 39065, F5, 20, 20) (dual of [(39065, 20), 781168, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(5132, 390650, F5, 20) (dual of [390650, 390518, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5132, 390652, F5, 20) (dual of [390652, 390520, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(5129, 390625, F5, 21) (dual of [390625, 390496, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(5105, 390625, F5, 17) (dual of [390625, 390520, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(53, 27, F5, 2) (dual of [27, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(5132, 390652, F5, 20) (dual of [390652, 390520, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(5132, 390650, F5, 20) (dual of [390650, 390518, 21]-code), using
(112, 112+20, 230672)-Net over F5 — Digital
Digital (112, 132, 230672)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5132, 230672, F5, 20) (dual of [230672, 230540, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5132, 390652, F5, 20) (dual of [390652, 390520, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(5129, 390625, F5, 21) (dual of [390625, 390496, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(5105, 390625, F5, 17) (dual of [390625, 390520, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(53, 27, F5, 2) (dual of [27, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(5132, 390652, F5, 20) (dual of [390652, 390520, 21]-code), using
(112, 112+20, large)-Net in Base 5 — Upper bound on s
There is no (112, 132, large)-net in base 5, because
- 18 times m-reduction [i] would yield (112, 114, large)-net in base 5, but