Best Known (50, 50+13, s)-Nets in Base 7
(50, 50+13, 2814)-Net over F7 — Constructive and digital
Digital (50, 63, 2814)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 13)-net over F7, using
- 6 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (43, 56, 2801)-net over F7, using
- net defined by OOA [i] based on linear OOA(756, 2801, F7, 13, 13) (dual of [(2801, 13), 36357, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using
- net defined by OOA [i] based on linear OOA(756, 2801, F7, 13, 13) (dual of [(2801, 13), 36357, 14]-NRT-code), using
- digital (1, 7, 13)-net over F7, using
(50, 50+13, 24103)-Net over F7 — Digital
Digital (50, 63, 24103)-net over F7, using
(50, 50+13, large)-Net in Base 7 — Upper bound on s
There is no (50, 63, large)-net in base 7, because
- 11 times m-reduction [i] would yield (50, 52, large)-net in base 7, but