Best Known (103−8, 103, s)-Nets in Base 5
(103−8, 103, 8388600)-Net over F5 — Constructive and digital
Digital (95, 103, 8388600)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (27, 31, 4194301)-net over F5, using
- net defined by OOA [i] based on linear OOA(531, 4194301, F5, 4, 4) (dual of [(4194301, 4), 16777173, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(531, 4194301, F5, 3, 4) (dual of [(4194301, 3), 12582872, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(531, 8388602, F5, 4) (dual of [8388602, 8388571, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(531, large, F5, 4) (dual of [large, large−31, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(531, large, F5, 4) (dual of [large, large−31, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(531, 8388602, F5, 4) (dual of [8388602, 8388571, 5]-code), using
- appending kth column [i] based on linear OOA(531, 4194301, F5, 3, 4) (dual of [(4194301, 3), 12582872, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(531, 4194301, F5, 4, 4) (dual of [(4194301, 4), 16777173, 5]-NRT-code), using
- digital (64, 72, 4194300)-net over F5, using
- net defined by OOA [i] based on linear OOA(572, 4194300, F5, 10, 8) (dual of [(4194300, 10), 41942928, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(572, 8388601, F5, 2, 8) (dual of [(8388601, 2), 16777130, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(572, 8388602, F5, 2, 8) (dual of [(8388602, 2), 16777132, 9]-NRT-code), using
- trace code [i] based on linear OOA(2536, 4194301, F25, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2536, 8388602, F25, 8) (dual of [8388602, 8388566, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
- OOA 2-folding [i] based on linear OA(2536, 8388602, F25, 8) (dual of [8388602, 8388566, 9]-code), using
- trace code [i] based on linear OOA(2536, 4194301, F25, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(572, 8388602, F5, 2, 8) (dual of [(8388602, 2), 16777132, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(572, 8388601, F5, 2, 8) (dual of [(8388601, 2), 16777130, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(572, 4194300, F5, 10, 8) (dual of [(4194300, 10), 41942928, 9]-NRT-code), using
- digital (27, 31, 4194301)-net over F5, using
(103−8, 103, large)-Net over F5 — Digital
Digital (95, 103, large)-net over F5, using
- 53 times duplication [i] based on digital (92, 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
(103−8, 103, large)-Net in Base 5 — Upper bound on s
There is no (95, 103, large)-net in base 5, because
- 6 times m-reduction [i] would yield (95, 97, large)-net in base 5, but