MinT - Best Known (149−47, 149, s)-Nets in Base 3

Best Known (149−47, 149, s)-Nets in Base 3

(149−47, 149, 156)-Net over F₃ — Constructive and digital

Digital (102, 149, 156)-net over F₃, using

11 times m-reduction [i] based on digital (102, 160, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 80, 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]

(149−47, 149, 294)-Net over F₃ — Digital

Digital (102, 149, 294)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−47, 149, 5518)-Net in Base 3 — Upper bound on s

There is no (102, 149, 5519)-net in base 3, because

1 times m-reduction [i] would yield (102, 148, 5519)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41167 596530 826684 014475 049960 348870 472770 400754 263006 202926 836159 813395 > 3¹⁴⁸ [i]