Best Known (7, 26, s)-Nets in Base 3
(7, 26, 16)-Net over F3 — Constructive and digital
Digital (7, 26, 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, 26, 27)-Net over F3 — Upper bound on s (digital)
There is no digital (7, 26, 28)-net over F3, because
- 4 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, 26, 30)-Net in Base 3 — Upper bound on s
There is no (7, 26, 31)-net in base 3, because
- 1 times m-reduction [i] would yield (7, 25, 31)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(325, 31, S3, 18), but
- the linear programming bound shows that M ≥ 503 289434 009142 / 475 > 325 [i]
- extracting embedded orthogonal array [i] would yield OA(325, 31, S3, 18), but