Best Known (113, 134, s)-Nets in Base 5
(113, 134, 39065)-Net over F5 — Constructive and digital
Digital (113, 134, 39065)-net over F5, using
- 51 times duplication [i] based on digital (112, 133, 39065)-net over F5, using
- net defined by OOA [i] based on linear OOA(5133, 39065, F5, 21, 21) (dual of [(39065, 21), 820232, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5133, 390651, F5, 21) (dual of [390651, 390518, 22]-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(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(5133, 390651, F5, 21) (dual of [390651, 390518, 22]-code), using
- net defined by OOA [i] based on linear OOA(5133, 39065, F5, 21, 21) (dual of [(39065, 21), 820232, 22]-NRT-code), using
(113, 134, 195327)-Net over F5 — Digital
Digital (113, 134, 195327)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5134, 195327, F5, 2, 21) (dual of [(195327, 2), 390520, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5134, 390654, F5, 21) (dual of [390654, 390520, 22]-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(55, 29, F5, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(5134, 390654, F5, 21) (dual of [390654, 390520, 22]-code), using
(113, 134, large)-Net in Base 5 — Upper bound on s
There is no (113, 134, large)-net in base 5, because
- 19 times m-reduction [i] would yield (113, 115, large)-net in base 5, but