Best Known (110, 110+20, s)-Nets in Base 5
(110, 110+20, 39064)-Net over F5 — Constructive and digital
Digital (110, 130, 39064)-net over F5, using
- net defined by OOA [i] based on linear OOA(5130, 39064, F5, 20, 20) (dual of [(39064, 20), 781150, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(5130, 390640, F5, 20) (dual of [390640, 390510, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5130, 390642, F5, 20) (dual of [390642, 390512, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [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(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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 Ce(20) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5130, 390642, F5, 20) (dual of [390642, 390512, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(5130, 390640, F5, 20) (dual of [390640, 390510, 21]-code), using
(110, 110+20, 195321)-Net over F5 — Digital
Digital (110, 130, 195321)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5130, 195321, F5, 2, 20) (dual of [(195321, 2), 390512, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5130, 390642, F5, 20) (dual of [390642, 390512, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [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(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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 Ce(20) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(5130, 390642, F5, 20) (dual of [390642, 390512, 21]-code), using
(110, 110+20, large)-Net in Base 5 — Upper bound on s
There is no (110, 130, large)-net in base 5, because
- 18 times m-reduction [i] would yield (110, 112, large)-net in base 5, but