Best Known (100−18, 100, s)-Nets in Base 25
(100−18, 100, 932133)-Net over F25 — Constructive and digital
Digital (82, 100, 932133)-net over F25, using
- 251 times duplication [i] based on digital (81, 99, 932133)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (68, 86, 932067)-net over F25, using
- net defined by OOA [i] based on linear OOA(2586, 932067, F25, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2586, large, F25, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(2586, large, F25, 18) (dual of [large, large−86, 19]-code), using
- net defined by OOA [i] based on linear OOA(2586, 932067, F25, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- digital (4, 13, 66)-net over F25, using
- (u, u+v)-construction [i] based on
(100−18, 100, large)-Net over F25 — Digital
Digital (82, 100, large)-net over F25, using
- t-expansion [i] based on digital (81, 100, large)-net over F25, using
- 2 times m-reduction [i] based on digital (81, 102, large)-net over F25, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25102, large, F25, 21) (dual of [large, large−102, 22]-code), using
- 1 times code embedding in larger space [i] 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]
- 1 times code embedding in larger space [i] based on linear OA(25101, large, F25, 21) (dual of [large, large−101, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25102, large, F25, 21) (dual of [large, large−102, 22]-code), using
- 2 times m-reduction [i] based on digital (81, 102, large)-net over F25, using
(100−18, 100, large)-Net in Base 25 — Upper bound on s
There is no (82, 100, large)-net in base 25, because
- 16 times m-reduction [i] would yield (82, 84, large)-net in base 25, but