MinT - Best Known (139, 139+95, s)-Nets in Base 3

Best Known (139, 139+95, s)-Nets in Base 3

(139, 139+95, 156)-Net over F₃ — Constructive and digital

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
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(139, 139+95, 206)-Net over F₃ — Digital

Digital (139, 234, 206)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+95, 2083)-Net in Base 3 — Upper bound on s

There is no (139, 234, 2084)-net in base 3, because

1 times m-reduction [i] would yield (139, 233, 2084)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1480 348634 407607 055168 039456 850933 998296 345769 107095 722453 002104 449564 321087 855694 766135 874803 017721 314613 198001 > 3²³³ [i]