Best Known (77, 97, s)-Nets in Base 25
(77, 97, 838860)-Net over F25 — Constructive and digital
Digital (77, 97, 838860)-net over F25, using
- 251 times duplication [i] based on digital (76, 96, 838860)-net over F25, using
- net defined by OOA [i] based on linear OOA(2596, 838860, F25, 20, 20) (dual of [(838860, 20), 16777104, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2596, 8388600, F25, 20) (dual of [8388600, 8388504, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2596, large, F25, 20) (dual of [large, large−96, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2596, large, F25, 20) (dual of [large, large−96, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2596, 8388600, F25, 20) (dual of [8388600, 8388504, 21]-code), using
- net defined by OOA [i] based on linear OOA(2596, 838860, F25, 20, 20) (dual of [(838860, 20), 16777104, 21]-NRT-code), using
(77, 97, large)-Net over F25 — Digital
Digital (77, 97, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2597, large, F25, 20) (dual of [large, large−97, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2596, large, F25, 20) (dual of [large, large−96, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 1 times code embedding in larger space [i] based on linear OA(2596, large, F25, 20) (dual of [large, large−96, 21]-code), using
(77, 97, large)-Net in Base 25 — Upper bound on s
There is no (77, 97, large)-net in base 25, because
- 18 times m-reduction [i] would yield (77, 79, large)-net in base 25, but