Best Known (29−6, 29, s)-Nets in Base 5
(29−6, 29, 26041)-Net over F5 — Constructive and digital
Digital (23, 29, 26041)-net over F5, using
- net defined by OOA [i] based on linear OOA(529, 26041, F5, 6, 6) (dual of [(26041, 6), 156217, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(529, 78123, F5, 6) (dual of [78123, 78094, 7]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(529, 78123, F5, 6) (dual of [78123, 78094, 7]-code), using
(29−6, 29, 43228)-Net over F5 — Digital
Digital (23, 29, 43228)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(529, 43228, F5, 6) (dual of [43228, 43199, 7]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using
(29−6, 29, 2594379)-Net in Base 5 — Upper bound on s
There is no (23, 29, 2594380)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 186 264617 787407 305521 > 529 [i]