Best Known (8, 14, s)-Nets in Base 5
(8, 14, 59)-Net over F5 — Constructive and digital
Digital (8, 14, 59)-net over F5, using
- (u, u+v)-construction [i] based on
(8, 14, 102)-Net over F5 — Digital
Digital (8, 14, 102)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(514, 102, F5, 6) (dual of [102, 88, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(514, 129, F5, 6) (dual of [129, 115, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(513, 125, F5, 6) (dual of [125, 112, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(510, 125, F5, 4) (dual of [125, 115, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(51, 4, F5, 1) (dual of [4, 3, 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(5) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(514, 129, F5, 6) (dual of [129, 115, 7]-code), using
(8, 14, 828)-Net in Base 5 — Upper bound on s
There is no (8, 14, 829)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 6115 576109 > 514 [i]