Best Known (85, 102, s)-Nets in Base 25
(85, 102, 1049551)-Net over F25 — Constructive and digital
Digital (85, 102, 1049551)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (13, 21, 976)-net over F25, using
- net defined by OOA [i] based on linear OOA(2521, 976, F25, 8, 8) (dual of [(976, 8), 7787, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2521, 3904, F25, 8) (dual of [3904, 3883, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2521, 3906, F25, 8) (dual of [3906, 3885, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2521, 3904, F25, 8) (dual of [3904, 3883, 9]-code), using
- net defined by OOA [i] based on linear OOA(2521, 976, F25, 8, 8) (dual of [(976, 8), 7787, 9]-NRT-code), using
- digital (64, 81, 1048575)-net over F25, using
- net defined by OOA [i] based on linear OOA(2581, 1048575, F25, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2581, 8388601, F25, 17) (dual of [8388601, 8388520, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2581, large, F25, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2581, large, F25, 17) (dual of [large, large−81, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2581, 8388601, F25, 17) (dual of [8388601, 8388520, 18]-code), using
- net defined by OOA [i] based on linear OOA(2581, 1048575, F25, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- digital (13, 21, 976)-net over F25, using
(85, 102, large)-Net over F25 — Digital
Digital (85, 102, large)-net over F25, using
- 5 times m-reduction [i] based on digital (85, 107, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25107, large, F25, 22) (dual of [large, large−107, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(25106, large, F25, 22) (dual of [large, large−106, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 1 times code embedding in larger space [i] based on linear OA(25106, large, F25, 22) (dual of [large, large−106, 23]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25107, large, F25, 22) (dual of [large, large−107, 23]-code), using
(85, 102, large)-Net in Base 25 — Upper bound on s
There is no (85, 102, large)-net in base 25, because
- 15 times m-reduction [i] would yield (85, 87, large)-net in base 25, but