Best Known (14, 44, s)-Nets in Base 3
(14, 44, 24)-Net over F3 — Constructive and digital
Digital (14, 44, 24)-net over F3, using
- t-expansion [i] based on digital (13, 44, 24)-net over F3, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 13 and N(F) ≥ 24, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
(14, 44, 49)-Net over F3 — Upper bound on s (digital)
There is no digital (14, 44, 50)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(344, 50, F3, 30) (dual of [50, 6, 31]-code), but
- “HJL†bound on codes from Brouwer’s database [i]
(14, 44, 53)-Net in Base 3 — Upper bound on s
There is no (14, 44, 54)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(344, 54, S3, 30), but
- the linear programming bound shows that M ≥ 12540 959946 988972 873227 479781 / 10 308089 > 344 [i]