MinT - Best Known (154−55, 154, s)-Nets in Base 3

Best Known (154−55, 154, s)-Nets in Base 3

(154−55, 154, 156)-Net over F₃ — Constructive and digital

Digital (99, 154, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 77, 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]

(154−55, 154, 207)-Net over F₃ — Digital

Digital (99, 154, 207)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−55, 154, 2734)-Net in Base 3 — Upper bound on s

There is no (99, 154, 2735)-net in base 3, because

1 times m-reduction [i] would yield (99, 153, 2735)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 029847 785600 266007 784272 462871 783298 330061 476730 136326 432180 225085 758091 > 3¹⁵³ [i]