Best Known (24, 30, s)-Nets in Base 5
(24, 30, 26044)-Net over F5 — Constructive and digital
Digital (24, 30, 26044)-net over F5, using
- net defined by OOA [i] based on linear OOA(530, 26044, F5, 6, 6) (dual of [(26044, 6), 156234, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(530, 78132, F5, 6) (dual of [78132, 78102, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(530, 78133, F5, 6) (dual of [78133, 78103, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(522, 78125, F5, 4) (dual of [78125, 78103, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(51, 8, F5, 1) (dual of [8, 7, 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(530, 78133, F5, 6) (dual of [78133, 78103, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(530, 78132, F5, 6) (dual of [78132, 78102, 7]-code), using
(24, 30, 64642)-Net over F5 — Digital
Digital (24, 30, 64642)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(530, 64642, F5, 6) (dual of [64642, 64612, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(530, 78133, F5, 6) (dual of [78133, 78103, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(522, 78125, F5, 4) (dual of [78125, 78103, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(51, 8, F5, 1) (dual of [8, 7, 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(530, 78133, F5, 6) (dual of [78133, 78103, 7]-code), using
(24, 30, 4436327)-Net in Base 5 — Upper bound on s
There is no (24, 30, 4436328)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 931 322686 501686 972065 > 530 [i]