Best Known (29, 38, s)-Nets in Base 25
(29, 38, 97684)-Net over F25 — Constructive and digital
Digital (29, 38, 97684)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, 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 (1, 5, 27)-net over F25, using
(29, 38, 685009)-Net over F25 — Digital
Digital (29, 38, 685009)-net over F25, using
(29, 38, large)-Net in Base 25 — Upper bound on s
There is no (29, 38, large)-net in base 25, because
- 7 times m-reduction [i] would yield (29, 31, large)-net in base 25, but