Best Known (7, 7+16, s)-Nets in Base 3
(7, 7+16, 16)-Net over F3 — Constructive and digital
Digital (7, 23, 16)-net over F3, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
(7, 7+16, 27)-Net over F3 — Upper bound on s (digital)
There is no digital (7, 23, 28)-net over F3, because
- 1 times m-reduction [i] would yield digital (7, 22, 28)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- “HHM†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
(7, 7+16, 34)-Net in Base 3 — Upper bound on s
There is no (7, 23, 35)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(323, 35, S3, 16), but
- the linear programming bound shows that M ≥ 16860 196039 306257 / 160225 > 323 [i]