Best Known (15−14, 15, s)-Nets in Base 9
(15−14, 15, 16)-Net over F9 — Constructive and digital
Digital (1, 15, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
(15−14, 15, 16)-Net over F9 — Upper bound on s (digital)
There is no digital (1, 15, 17)-net over F9, because
- 4 times m-reduction [i] would yield digital (1, 11, 17)-net over F9, but
- extracting embedded orthogonal array [i] would yield linear OA(911, 17, F9, 10) (dual of [17, 6, 11]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(911, 17, F9, 10) (dual of [17, 6, 11]-code), but
(15−14, 15, 26)-Net in Base 9 — Upper bound on s
There is no (1, 15, 27)-net in base 9, because
- extracting embedded OOA [i] would yield OOA(915, 27, S9, 2, 14), but
- the linear programming bound for OOAs shows that M ≥ 403188 041516 503853 175648 662277 / 1930 048540 098197 > 915 [i]