Best Known (23, 29, s)-Nets in Base 49
(23, 29, 3843206)-Net over F49 — Constructive and digital
Digital (23, 29, 3843206)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (4, 7, 5769603)-net over F49, using
- net defined by OOA [i] based on linear OOA(497, 5769603, F49, 3, 3) (dual of [(5769603, 3), 17308802, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(497, 5769603, F49, 2, 3) (dual of [(5769603, 2), 11539199, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(497, 5769603, F49, 3, 3) (dual of [(5769603, 3), 17308802, 4]-NRT-code), using
- digital (16, 22, 1921603)-net over F49, using
- net defined by OOA [i] based on linear OOA(4922, 1921603, F49, 6, 6) (dual of [(1921603, 6), 11529596, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(4922, 5764809, F49, 6) (dual of [5764809, 5764787, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(4922, 5764810, F49, 6) (dual of [5764810, 5764788, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 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(5) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(4922, 5764810, F49, 6) (dual of [5764810, 5764788, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(4922, 5764809, F49, 6) (dual of [5764809, 5764787, 7]-code), using
- net defined by OOA [i] based on linear OOA(4922, 1921603, F49, 6, 6) (dual of [(1921603, 6), 11529596, 7]-NRT-code), using
- digital (4, 7, 5769603)-net over F49, using
(23, 29, large)-Net over F49 — Digital
Digital (23, 29, large)-net over F49, using
- t-expansion [i] based on digital (22, 29, large)-net over F49, using
(23, 29, large)-Net in Base 49 — Upper bound on s
There is no (23, 29, large)-net in base 49, because
- 4 times m-reduction [i] would yield (23, 25, large)-net in base 49, but