Best Known (64, 79, s)-Nets in Base 25
(64, 79, 1198398)-Net over F25 — Constructive and digital
Digital (64, 79, 1198398)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (56, 71, 1198371)-net over F25, using
- net defined by OOA [i] based on linear OOA(2571, 1198371, F25, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2571, 8388598, F25, 15) (dual of [8388598, 8388527, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2571, large, F25, 15) (dual of [large, large−71, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2571, large, F25, 15) (dual of [large, large−71, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2571, 8388598, F25, 15) (dual of [8388598, 8388527, 16]-code), using
- net defined by OOA [i] based on linear OOA(2571, 1198371, F25, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
- digital (1, 8, 27)-net over F25, using
(64, 79, large)-Net over F25 — Digital
Digital (64, 79, large)-net over F25, using
- 252 times duplication [i] based on digital (62, 77, large)-net over F25, using
- t-expansion [i] based on digital (61, 77, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2577, large, F25, 16) (dual of [large, large−77, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 1 times code embedding in larger space [i] based on linear OA(2576, large, F25, 16) (dual of [large, large−76, 17]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2577, large, F25, 16) (dual of [large, large−77, 17]-code), using
- t-expansion [i] based on digital (61, 77, large)-net over F25, using
(64, 79, large)-Net in Base 25 — Upper bound on s
There is no (64, 79, large)-net in base 25, because
- 13 times m-reduction [i] would yield (64, 66, large)-net in base 25, but