Best Known (29, 36, s)-Nets in Base 5
(29, 36, 26043)-Net over F5 — Constructive and digital
Digital (29, 36, 26043)-net over F5, using
- net defined by OOA [i] based on linear OOA(536, 26043, F5, 7, 7) (dual of [(26043, 7), 182265, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(536, 78130, F5, 7) (dual of [78130, 78094, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(536, 78132, F5, 7) (dual of [78132, 78096, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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(50, 7, F5, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(536, 78132, F5, 7) (dual of [78132, 78096, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(536, 78130, F5, 7) (dual of [78130, 78094, 8]-code), using
(29, 36, 50879)-Net over F5 — Digital
Digital (29, 36, 50879)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(536, 50879, F5, 7) (dual of [50879, 50843, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using
- an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(536, 78125, F5, 7) (dual of [78125, 78089, 8]-code), using
(29, 36, large)-Net in Base 5 — Upper bound on s
There is no (29, 36, large)-net in base 5, because
- 5 times m-reduction [i] would yield (29, 31, large)-net in base 5, but