Best Known (22, 22+9, s)-Nets in Base 49
(22, 22+9, 30588)-Net over F49 — Constructive and digital
Digital (22, 31, 30588)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 1176)-net over F49, using
- net defined by OOA [i] based on linear OOA(496, 1176, F49, 4, 4) (dual of [(1176, 4), 4698, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(496, 1176, F49, 3, 4) (dual of [(1176, 3), 3522, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(496, 2352, F49, 4) (dual of [2352, 2346, 5]-code), using
- 1 times truncation [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(496, 2352, F49, 4) (dual of [2352, 2346, 5]-code), using
- appending kth column [i] based on linear OOA(496, 1176, F49, 3, 4) (dual of [(1176, 3), 3522, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(496, 1176, F49, 4, 4) (dual of [(1176, 4), 4698, 5]-NRT-code), using
- digital (16, 25, 29412)-net over F49, using
- net defined by OOA [i] based on linear OOA(4925, 29412, F49, 9, 9) (dual of [(29412, 9), 264683, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(4925, 117649, F49, 9) (dual of [117649, 117624, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(4925, 117649, F49, 9) (dual of [117649, 117624, 10]-code), using
- net defined by OOA [i] based on linear OOA(4925, 29412, F49, 9, 9) (dual of [(29412, 9), 264683, 10]-NRT-code), using
- digital (2, 6, 1176)-net over F49, using
(22, 22+9, 277949)-Net over F49 — Digital
Digital (22, 31, 277949)-net over F49, using
(22, 22+9, large)-Net in Base 49 — Upper bound on s
There is no (22, 31, large)-net in base 49, because
- 7 times m-reduction [i] would yield (22, 24, large)-net in base 49, but