Best Known (87, 87+18, s)-Nets in Base 25
(87, 87+18, 932225)-Net over F25 — Constructive and digital
Digital (87, 105, 932225)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (10, 19, 158)-net over F25, using
- net defined by OOA [i] based on linear OOA(2519, 158, F25, 9, 9) (dual of [(158, 9), 1403, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2519, 633, F25, 9) (dual of [633, 614, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [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]
- linear OA(2511, 625, F25, 6) (dual of [625, 614, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(2519, 633, F25, 9) (dual of [633, 614, 10]-code), using
- net defined by OOA [i] based on linear OOA(2519, 158, F25, 9, 9) (dual of [(158, 9), 1403, 10]-NRT-code), 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 (10, 19, 158)-net over F25, using
(87, 87+18, large)-Net over F25 — Digital
Digital (87, 105, large)-net over F25, using
- t-expansion [i] based on digital (85, 105, large)-net over F25, using
- 2 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
- 2 times m-reduction [i] based on digital (85, 107, large)-net over F25, using
(87, 87+18, large)-Net in Base 25 — Upper bound on s
There is no (87, 105, large)-net in base 25, because
- 16 times m-reduction [i] would yield (87, 89, large)-net in base 25, but