Best Known (33, 43, s)-Nets in Base 49
(33, 43, 1153012)-Net over F49 — Constructive and digital
Digital (33, 43, 1153012)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (27, 37, 1152961)-net over F49, using
- net defined by OOA [i] based on linear OOA(4937, 1152961, F49, 10, 10) (dual of [(1152961, 10), 11529573, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(4937, 5764805, F49, 10) (dual of [5764805, 5764768, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(4937, 5764801, F49, 10) (dual of [5764801, 5764764, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- OA 5-folding and stacking [i] based on linear OA(4937, 5764805, F49, 10) (dual of [5764805, 5764768, 11]-code), using
- net defined by OOA [i] based on linear OOA(4937, 1152961, F49, 10, 10) (dual of [(1152961, 10), 11529573, 11]-NRT-code), using
- digital (1, 6, 51)-net over F49, using
(33, 43, large)-Net over F49 — Digital
Digital (33, 43, large)-net over F49, using
(33, 43, large)-Net in Base 49 — Upper bound on s
There is no (33, 43, large)-net in base 49, because
- 8 times m-reduction [i] would yield (33, 35, large)-net in base 49, but