Best Known (40−11, 40, s)-Nets in Base 49
(40−11, 40, 24756)-Net over F49 — Constructive and digital
Digital (29, 40, 24756)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (4, 9, 1226)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 50)-net over F49, using
- 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
- (u, u+v)-construction [i] based on
- digital (20, 31, 23530)-net over F49, using
- net defined by OOA [i] based on linear OOA(4931, 23530, F49, 11, 11) (dual of [(23530, 11), 258799, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4931, 117651, F49, 11) (dual of [117651, 117620, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4931, 117652, F49, 11) (dual of [117652, 117621, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(4931, 117649, F49, 11) (dual of [117649, 117618, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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(490, 3, F49, 0) (dual of [3, 3, 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(10) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(4931, 117652, F49, 11) (dual of [117652, 117621, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4931, 117651, F49, 11) (dual of [117651, 117620, 12]-code), using
- net defined by OOA [i] based on linear OOA(4931, 23530, F49, 11, 11) (dual of [(23530, 11), 258799, 12]-NRT-code), using
- digital (4, 9, 1226)-net over F49, using
(40−11, 40, 543905)-Net over F49 — Digital
Digital (29, 40, 543905)-net over F49, using
(40−11, 40, large)-Net in Base 49 — Upper bound on s
There is no (29, 40, large)-net in base 49, because
- 9 times m-reduction [i] would yield (29, 31, large)-net in base 49, but