Best Known (95, 95+10, s)-Nets in Base 5
(95, 95+10, 3355740)-Net over F5 — Constructive and digital
Digital (95, 105, 3355740)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (8, 13, 300)-net over F5, using
- net defined by OOA [i] based on linear OOA(513, 300, F5, 5, 5) (dual of [(300, 5), 1487, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(513, 601, F5, 5) (dual of [601, 588, 6]-code), using
- net defined by OOA [i] based on linear OOA(513, 300, F5, 5, 5) (dual of [(300, 5), 1487, 6]-NRT-code), using
- digital (82, 92, 3355440)-net over F5, using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F25, using
- digital (8, 13, 300)-net over F5, using
(95, 95+10, large)-Net over F5 — Digital
Digital (95, 105, large)-net over F5, using
- 55 times duplication [i] based on digital (90, 100, large)-net over F5, using
- t-expansion [i] based on digital (88, 100, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5100, large, F5, 12) (dual of [large, large−100, 13]-code), using
- 9 times code embedding in larger space [i] based on linear OA(591, large, F5, 12) (dual of [large, large−91, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 9 times code embedding in larger space [i] based on linear OA(591, large, F5, 12) (dual of [large, large−91, 13]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5100, large, F5, 12) (dual of [large, large−100, 13]-code), using
- t-expansion [i] based on digital (88, 100, large)-net over F5, using
(95, 95+10, large)-Net in Base 5 — Upper bound on s
There is no (95, 105, large)-net in base 5, because
- 8 times m-reduction [i] would yield (95, 97, large)-net in base 5, but