Best Known (48−11, 48, s)-Nets in Base 49
(48−11, 48, 1154136)-Net over F49 — Constructive and digital
Digital (37, 48, 1154136)-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 (30, 41, 1152960)-net over F49, using
- net defined by OOA [i] based on linear OOA(4941, 1152960, F49, 11, 11) (dual of [(1152960, 11), 12682519, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using
- net defined by OOA [i] based on linear OOA(4941, 1152960, F49, 11, 11) (dual of [(1152960, 11), 12682519, 12]-NRT-code), using
- digital (2, 7, 1176)-net over F49, using
(48−11, 48, large)-Net over F49 — Digital
Digital (37, 48, large)-net over F49, using
(48−11, 48, large)-Net in Base 49 — Upper bound on s
There is no (37, 48, large)-net in base 49, because
- 9 times m-reduction [i] would yield (37, 39, large)-net in base 49, but