Best Known (2, 7, s)-Nets in Base 9
(2, 7, 36)-Net over F9 — Constructive and digital
Digital (2, 7, 36)-net over F9, using
- net defined by OOA [i] based on linear OOA(97, 36, F9, 5, 5) (dual of [(36, 5), 173, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
(2, 7, 128)-Net in Base 9 — Upper bound on s
There is no (2, 7, 129)-net in base 9, because
- 1 times m-reduction [i] would yield (2, 6, 129)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 538705 > 96 [i]
- extracting embedded orthogonal array [i] would yield OA(96, 129, S9, 4), but
- the linear programming bound shows that M ≥ 10240 704045 / 19093 > 96 [i]