Best Known (83−73, 83, s)-Nets in Base 3
(83−73, 83, 19)-Net over F3 — Constructive and digital
Digital (10, 83, 19)-net over F3, using
- t-expansion [i] based on digital (9, 83, 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
- net from sequence [i] based on digital (9, 18)-sequence over F3, using
(83−73, 83, 20)-Net over F3 — Digital
Digital (10, 83, 20)-net over F3, using
- net from sequence [i] based on digital (10, 19)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 10 and N(F) ≥ 20, using
(83−73, 83, 28)-Net in Base 3 — Upper bound on s
There is no (10, 83, 29)-net in base 3, because
- extracting embedded OOA [i] would yield OOA(383, 29, S3, 3, 73), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 155642 697373 306257 251835 620347 321612 373853 / 37 > 383 [i]