Best Known (139, 227, s)-Nets in Base 3
(139, 227, 156)-Net over F3 — Constructive and digital
Digital (139, 227, 156)-net over F3, using
- 7 times m-reduction [i] based on digital (139, 234, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 117, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- trace code for nets [i] based on digital (22, 117, 78)-net over F9, using
(139, 227, 228)-Net over F3 — Digital
Digital (139, 227, 228)-net over F3, using
(139, 227, 2453)-Net in Base 3 — Upper bound on s
There is no (139, 227, 2454)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 035003 876792 893739 051196 014308 377405 944906 904776 637447 978269 548441 283283 861501 158771 106802 988006 055683 789209 > 3227 [i]