Best Known (35, 35+10, s)-Nets in Base 25
(35, 35+10, 78426)-Net over F25 — Constructive and digital
Digital (35, 45, 78426)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 300)-net over F25, using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- digital (28, 38, 78126)-net over F25, using
- net defined by OOA [i] based on linear OOA(2538, 78126, F25, 10, 10) (dual of [(78126, 10), 781222, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2538, 390630, F25, 10) (dual of [390630, 390592, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2538, 390634, F25, 10) (dual of [390634, 390596, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(2537, 390625, F25, 10) (dual of [390625, 390588, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(2538, 390634, F25, 10) (dual of [390634, 390596, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2538, 390630, F25, 10) (dual of [390630, 390592, 11]-code), using
- net defined by OOA [i] based on linear OOA(2538, 78126, F25, 10, 10) (dual of [(78126, 10), 781222, 11]-NRT-code), using
- digital (2, 7, 300)-net over F25, using
(35, 35+10, 1687491)-Net over F25 — Digital
Digital (35, 45, 1687491)-net over F25, using
(35, 35+10, large)-Net in Base 25 — Upper bound on s
There is no (35, 45, large)-net in base 25, because
- 8 times m-reduction [i] would yield (35, 37, large)-net in base 25, but