Best Known (33−6, 33, s)-Nets in Base 49
(33−6, 33, 5764803)-Net over F49 — Constructive and digital
Digital (27, 33, 5764803)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (3, 5, 1921601)-net over F49, using
- s-reduction based on digital (3, 5, 5884901)-net over F49, using
- digital (4, 7, 1921601)-net over F49, using
- s-reduction 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
- s-reduction based on digital (4, 7, 5769603)-net over F49, using
- digital (15, 21, 1921601)-net over F49, using
- net defined by OOA [i] based on linear OOA(4921, 1921601, F49, 6, 6) (dual of [(1921601, 6), 11529585, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(4921, 5764803, F49, 6) (dual of [5764803, 5764782, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(4921, 5764805, F49, 6) (dual of [5764805, 5764784, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [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(4917, 5764801, F49, 5) (dual of [5764801, 5764784, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(4921, 5764805, F49, 6) (dual of [5764805, 5764784, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(4921, 5764803, F49, 6) (dual of [5764803, 5764782, 7]-code), using
- net defined by OOA [i] based on linear OOA(4921, 1921601, F49, 6, 6) (dual of [(1921601, 6), 11529585, 7]-NRT-code), using
- digital (3, 5, 1921601)-net over F49, using
(33−6, 33, large)-Net over F49 — Digital
Digital (27, 33, large)-net over F49, using
- t-expansion [i] based on digital (26, 33, large)-net over F49, using
- 1 times m-reduction [i] based on digital (26, 34, large)-net over F49, using
(33−6, 33, large)-Net in Base 49 — Upper bound on s
There is no (27, 33, large)-net in base 49, because
- 4 times m-reduction [i] would yield (27, 29, large)-net in base 49, but