MinT - Best Known (139−43, 139, s)-Nets in Base 3

Best Known (139−43, 139, s)-Nets in Base 3

(139−43, 139, 156)-Net over F₃ — Constructive and digital

Digital (96, 139, 156)-net over F₃, using

9 times m-reduction [i] based on digital (96, 148, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 74, 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]

(139−43, 139, 295)-Net over F₃ — Digital

Digital (96, 139, 295)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−43, 139, 5906)-Net in Base 3 — Upper bound on s

There is no (96, 139, 5907)-net in base 3, because

1 times m-reduction [i] would yield (96, 138, 5907)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 697498 467976 725612 539923 342254 107044 736113 995122 929592 836906 228095 > 3¹³⁸ [i]