Best Known (7−5, 7, s)-Nets in Base 7
(7−5, 7, 21)-Net over F7 — Constructive and digital
Digital (2, 7, 21)-net over F7, using
- net defined by OOA [i] based on linear OOA(77, 21, F7, 5, 5) (dual of [(21, 5), 98, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
(7−5, 7, 79)-Net in Base 7 — Upper bound on s
There is no (2, 7, 80)-net in base 7, because
- 1 times m-reduction [i] would yield (2, 6, 80)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(76, 80, S7, 4), but
- the linear programming bound shows that M ≥ 31 342311 / 263 > 76 [i]
- extracting embedded orthogonal array [i] would yield OA(76, 80, S7, 4), but