Best Known (75, 87, s)-Nets in Base 5
(75, 87, 325526)-Net over F5 — Constructive and digital
Digital (75, 87, 325526)-net over F5, using
- net defined by OOA [i] based on linear OOA(587, 325526, F5, 12, 12) (dual of [(325526, 12), 3906225, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(587, 1953156, F5, 12) (dual of [1953156, 1953069, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(587, 1953157, F5, 12) (dual of [1953157, 1953070, 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(55, 32, F5, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(587, 1953157, F5, 12) (dual of [1953157, 1953070, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(587, 1953156, F5, 12) (dual of [1953156, 1953069, 13]-code), using
(75, 87, 1161598)-Net over F5 — Digital
Digital (75, 87, 1161598)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(587, 1161598, F5, 12) (dual of [1161598, 1161511, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(587, 1953157, F5, 12) (dual of [1953157, 1953070, 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(55, 32, F5, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(587, 1953157, F5, 12) (dual of [1953157, 1953070, 13]-code), using
(75, 87, large)-Net in Base 5 — Upper bound on s
There is no (75, 87, large)-net in base 5, because
- 10 times m-reduction [i] would yield (75, 77, large)-net in base 5, but