MinT - Best Known (238−93, 238, s)-Nets in Base 3

Best Known (238−93, 238, s)-Nets in Base 3

(238−93, 238, 156)-Net over F₃ — Constructive and digital

Digital (145, 238, 156)-net over F₃, using

8 times m-reduction [i] based on digital (145, 246, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 123, 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]

(238−93, 238, 232)-Net over F₃ — Digital

Digital (145, 238, 232)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−93, 238, 2539)-Net in Base 3 — Upper bound on s

There is no (145, 238, 2540)-net in base 3, because

1 times m-reduction [i] would yield (145, 237, 2540)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 120587 208642 843506 939055 304017 245325 490249 912984 859541 931541 539076 231081 161947 057927 102292 365982 458455 934671 856585 > 3²³⁷ [i]