Best Known (9, 31, s)-Nets in Base 3
(9, 31, 19)-Net over F3 — Constructive and digital
Digital (9, 31, 19)-net over F3, using
- net from sequence [i] based on digital (9, 18)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using
(9, 31, 34)-Net over F3 — Upper bound on s (digital)
There is no digital (9, 31, 35)-net over F3, because
- 4 times m-reduction [i] would yield digital (9, 27, 35)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(327, 35, F3, 18) (dual of [35, 8, 19]-code), but
- residual code [i] would yield linear OA(39, 16, F3, 6) (dual of [16, 7, 7]-code), but
- “vE2†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(39, 16, F3, 6) (dual of [16, 7, 7]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(327, 35, F3, 18) (dual of [35, 8, 19]-code), but
(9, 31, 36)-Net in Base 3 — Upper bound on s
There is no (9, 31, 37)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(331, 37, S3, 22), but
- the linear programming bound shows that M ≥ 450283 905890 997363 / 667 > 331 [i]