Best Known (26, 26+10, s)-Nets in Base 49
(26, 26+10, 24707)-Net over F49 — Constructive and digital
Digital (26, 36, 24707)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 1176)-net over F49, using
- net defined by OOA [i] based on linear OOA(497, 1176, F49, 5, 5) (dual of [(1176, 5), 5873, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- net defined by OOA [i] based on linear OOA(497, 1176, F49, 5, 5) (dual of [(1176, 5), 5873, 6]-NRT-code), using
- digital (19, 29, 23531)-net over F49, using
- net defined by OOA [i] based on linear OOA(4929, 23531, F49, 10, 10) (dual of [(23531, 10), 235281, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(4929, 117655, F49, 10) (dual of [117655, 117626, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4929, 117656, F49, 10) (dual of [117656, 117627, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(4928, 117649, F49, 10) (dual of [117649, 117621, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4922, 117649, F49, 8) (dual of [117649, 117627, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 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(4929, 117656, F49, 10) (dual of [117656, 117627, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(4929, 117655, F49, 10) (dual of [117655, 117626, 11]-code), using
- net defined by OOA [i] based on linear OOA(4929, 23531, F49, 10, 10) (dual of [(23531, 10), 235281, 11]-NRT-code), using
- digital (2, 7, 1176)-net over F49, using
(26, 26+10, 498079)-Net over F49 — Digital
Digital (26, 36, 498079)-net over F49, using
(26, 26+10, large)-Net in Base 49 — Upper bound on s
There is no (26, 36, large)-net in base 49, because
- 8 times m-reduction [i] would yield (26, 28, large)-net in base 49, but