Best Known (39−9, 39, s)-Nets in Base 25
(39−9, 39, 97957)-Net over F25 — Constructive and digital
Digital (30, 39, 97957)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 300)-net over F25, using
- net defined by OOA [i] based on linear OOA(256, 300, F25, 4, 4) (dual of [(300, 4), 1194, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(256, 600, F25, 4) (dual of [600, 594, 5]-code), using
- 1 times truncation [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(256, 600, F25, 4) (dual of [600, 594, 5]-code), using
- net defined by OOA [i] based on linear OOA(256, 300, F25, 4, 4) (dual of [(300, 4), 1194, 5]-NRT-code), using
- digital (24, 33, 97657)-net over F25, using
- net defined by OOA [i] based on linear OOA(2533, 97657, F25, 9, 9) (dual of [(97657, 9), 878880, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2533, 390629, F25, 9) (dual of [390629, 390596, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(2533, 390625, F25, 9) (dual of [390625, 390592, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2529, 390625, F25, 8) (dual of [390625, 390596, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(2533, 390629, F25, 9) (dual of [390629, 390596, 10]-code), using
- net defined by OOA [i] based on linear OOA(2533, 97657, F25, 9, 9) (dual of [(97657, 9), 878880, 10]-NRT-code), using
- digital (2, 6, 300)-net over F25, using
(39−9, 39, 1024326)-Net over F25 — Digital
Digital (30, 39, 1024326)-net over F25, using
(39−9, 39, large)-Net in Base 25 — Upper bound on s
There is no (30, 39, large)-net in base 25, because
- 7 times m-reduction [i] would yield (30, 32, large)-net in base 25, but