Best Known (84, 93, s)-Nets in Base 5
(84, 93, 4194600)-Net over F5 — Constructive and digital
Digital (84, 93, 4194600)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (7, 11, 300)-net over F5, using
- net defined by OOA [i] based on linear OOA(511, 300, F5, 4, 4) (dual of [(300, 4), 1189, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(511, 300, F5, 3, 4) (dual of [(300, 3), 889, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(511, 600, F5, 4) (dual of [600, 589, 5]-code), using
- base reduction for projective spaces (embedding PG(5,25) in PG(10,5)) [i] based on linear OA(256, 600, F25, 4) (dual of [600, 594, 5]-code), using
- 1 times truncation [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- base reduction for projective spaces (embedding PG(5,25) in PG(10,5)) [i] based on linear OA(256, 600, F25, 4) (dual of [600, 594, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(511, 600, F5, 4) (dual of [600, 589, 5]-code), using
- appending kth column [i] based on linear OOA(511, 300, F5, 3, 4) (dual of [(300, 3), 889, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(511, 300, F5, 4, 4) (dual of [(300, 4), 1189, 5]-NRT-code), using
- digital (73, 82, 4194300)-net over F5, using
- net defined by OOA [i] based on linear OOA(582, 4194300, F5, 10, 9) (dual of [(4194300, 10), 41942918, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(582, 8388601, F5, 2, 9) (dual of [(8388601, 2), 16777120, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(582, 8388602, F5, 2, 9) (dual of [(8388602, 2), 16777122, 10]-NRT-code), using
- trace code [i] based on linear OOA(2541, 4194301, F25, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2541, 8388602, F25, 9) (dual of [8388602, 8388561, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- OOA 2-folding [i] based on linear OA(2541, 8388602, F25, 9) (dual of [8388602, 8388561, 10]-code), using
- trace code [i] based on linear OOA(2541, 4194301, F25, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(582, 8388602, F5, 2, 9) (dual of [(8388602, 2), 16777122, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(582, 8388601, F5, 2, 9) (dual of [(8388601, 2), 16777120, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(582, 4194300, F5, 10, 9) (dual of [(4194300, 10), 41942918, 10]-NRT-code), using
- digital (7, 11, 300)-net over F5, using
(84, 93, large)-Net over F5 — Digital
Digital (84, 93, large)-net over F5, using
- 53 times duplication [i] based on digital (81, 90, large)-net over F5, using
- t-expansion [i] based on digital (79, 90, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(590, large, F5, 11) (dual of [large, large−90, 12]-code), using
- 9 times code embedding in larger space [i] based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 9 times code embedding in larger space [i] based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(590, large, F5, 11) (dual of [large, large−90, 12]-code), using
- t-expansion [i] based on digital (79, 90, large)-net over F5, using
(84, 93, large)-Net in Base 5 — Upper bound on s
There is no (84, 93, large)-net in base 5, because
- 7 times m-reduction [i] would yield (84, 86, large)-net in base 5, but