Best Known (89, 89+18, s)-Nets in Base 25
(89, 89+18, 932249)-Net over F25 — Constructive and digital
Digital (89, 107, 932249)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (12, 21, 182)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (8, 17, 156)-net over F25, using
- net defined by OOA [i] based on linear OOA(2517, 156, F25, 9, 9) (dual of [(156, 9), 1387, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2517, 625, F25, 9) (dual of [625, 608, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(2517, 625, F25, 9) (dual of [625, 608, 10]-code), using
- net defined by OOA [i] based on linear OOA(2517, 156, F25, 9, 9) (dual of [(156, 9), 1387, 10]-NRT-code), using
- digital (0, 4, 26)-net over F25, using
- (u, u+v)-construction [i] based on
- 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 (12, 21, 182)-net over F25, using
(89, 89+18, large)-Net over F25 — Digital
Digital (89, 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
(89, 89+18, large)-Net in Base 25 — Upper bound on s
There is no (89, 107, large)-net in base 25, because
- 16 times m-reduction [i] would yield (89, 91, large)-net in base 25, but