MinT - Best Known (147, 147+103, s)-Nets in Base 3

Best Known (147, 147+103, s)-Nets in Base 3

(147, 147+103, 156)-Net over F₃ — Constructive and digital

Digital (147, 250, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 125, 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]

(147, 147+103, 209)-Net over F₃ — Digital

Digital (147, 250, 209)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+103, 2069)-Net in Base 3 — Upper bound on s

There is no (147, 250, 2070)-net in base 3, because

1 times m-reduction [i] would yield (147, 249, 2070)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63835 461190 686477 660825 371549 694622 853715 648613 749239 654917 392757 853202 220754 756836 418440 419018 595425 479650 899833 057217 > 3²⁴⁹ [i]