Best Known (249−65, 249, s)-Nets in Base 3
(249−65, 249, 324)-Net over F3 — Constructive and digital
Digital (184, 249, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 83, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
(249−65, 249, 865)-Net over F3 — Digital
Digital (184, 249, 865)-net over F3, using
(249−65, 249, 31850)-Net in Base 3 — Upper bound on s
There is no (184, 249, 31851)-net in base 3, because
- 1 times m-reduction [i] would yield (184, 248, 31851)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 21205 974562 360433 267013 774612 327914 099469 988039 913722 101245 075703 856902 852872 636055 500301 864359 330663 335784 365772 528577 > 3248 [i]