Best Known (74, 74+12, s)-Nets in Base 5
(74, 74+12, 325525)-Net over F5 — Constructive and digital
Digital (74, 86, 325525)-net over F5, using
- net defined by OOA [i] based on linear OOA(586, 325525, F5, 12, 12) (dual of [(325525, 12), 3906214, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(586, 1953150, F5, 12) (dual of [1953150, 1953064, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(586, 1953151, F5, 12) (dual of [1953151, 1953065, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(582, 1953125, F5, 12) (dual of [1953125, 1953043, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(555, 1953125, F5, 8) (dual of [1953125, 1953070, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(586, 1953151, F5, 12) (dual of [1953151, 1953065, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(586, 1953150, F5, 12) (dual of [1953150, 1953064, 13]-code), using
(74, 74+12, 988914)-Net over F5 — Digital
Digital (74, 86, 988914)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(586, 988914, F5, 12) (dual of [988914, 988828, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(586, 1953151, F5, 12) (dual of [1953151, 1953065, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(582, 1953125, F5, 12) (dual of [1953125, 1953043, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(555, 1953125, F5, 8) (dual of [1953125, 1953070, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(586, 1953151, F5, 12) (dual of [1953151, 1953065, 13]-code), using
(74, 74+12, large)-Net in Base 5 — Upper bound on s
There is no (74, 86, large)-net in base 5, because
- 10 times m-reduction [i] would yield (74, 76, large)-net in base 5, but