Best Known (7, 27, s)-Nets in Base 3
(7, 27, 16)-Net over F3 — Constructive and digital
Digital (7, 27, 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, 27, 27)-Net over F3 — Upper bound on s (digital)
There is no digital (7, 27, 28)-net over F3, because
- 5 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, 27, 29)-Net in Base 3 — Upper bound on s
There is no (7, 27, 30)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(327, 30, S3, 20), but
- the (dual) Plotkin bound shows that M ≥ 68 630377 364883 / 7 > 327 [i]