Best Known (109−20, 109, s)-Nets in Base 25
(109−20, 109, 838912)-Net over F25 — Constructive and digital
Digital (89, 109, 838912)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- 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
- digital (3, 13, 52)-net over F25, using
(109−20, 109, large)-Net over F25 — Digital
Digital (89, 109, large)-net over F25, using
- 252 times duplication [i] based on digital (87, 107, large)-net over F25, using
- t-expansion [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
- t-expansion [i] based on digital (85, 107, large)-net over F25, using
(109−20, 109, large)-Net in Base 25 — Upper bound on s
There is no (89, 109, large)-net in base 25, because
- 18 times m-reduction [i] would yield (89, 91, large)-net in base 25, but