Best Known (106−21, 106, s)-Nets in Base 25
(106−21, 106, 838860)-Net over F25 — Constructive and digital
Digital (85, 106, 838860)-net over F25, using
- 255 times duplication [i] based on digital (80, 101, 838860)-net over F25, using
- net defined by OOA [i] based on linear OOA(25101, 838860, F25, 21, 21) (dual of [(838860, 21), 17615959, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25101, 8388601, F25, 21) (dual of [8388601, 8388500, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25101, large, F25, 21) (dual of [large, large−101, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(25101, large, F25, 21) (dual of [large, large−101, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25101, 8388601, F25, 21) (dual of [8388601, 8388500, 22]-code), using
- net defined by OOA [i] based on linear OOA(25101, 838860, F25, 21, 21) (dual of [(838860, 21), 17615959, 22]-NRT-code), using
(106−21, 106, large)-Net over F25 — Digital
Digital (85, 106, large)-net over F25, using
- 1 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
(106−21, 106, large)-Net in Base 25 — Upper bound on s
There is no (85, 106, large)-net in base 25, because
- 19 times m-reduction [i] would yield (85, 87, large)-net in base 25, but