Best Known (12−3, 12, s)-Nets in Base 7
(12−3, 12, 1067080)-Net over F7 — Constructive and digital
Digital (9, 12, 1067080)-net over F7, using
- net defined by OOA [i] based on linear OOA(712, 1067080, F7, 3, 3) (dual of [(1067080, 3), 3201228, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(712, 1067080, F7, 2, 3) (dual of [(1067080, 2), 2134148, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(712, 1067080, F7, 3) (dual of [1067080, 1067068, 4]-code or 1067080-cap in PG(11,7)), using
- appending kth column [i] based on linear OOA(712, 1067080, F7, 2, 3) (dual of [(1067080, 2), 2134148, 4]-NRT-code), using
(12−3, 12, large)-Net in Base 7 — Upper bound on s
There is no (9, 12, large)-net in base 7, because
- 1 times m-reduction [i] would yield (9, 11, large)-net in base 7, but