MinT - Best Known (134, 134+73, s)-Nets in Base 3

Best Known (134, 134+73, s)-Nets in Base 3

(134, 134+73, 156)-Net over F₃ — Constructive and digital

Digital (134, 207, 156)-net over F₃, using

17 times m-reduction [i] based on digital (134, 224, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 112, 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]

(134, 134+73, 276)-Net over F₃ — Digital

Digital (134, 207, 276)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+73, 3800)-Net in Base 3 — Upper bound on s

There is no (134, 207, 3801)-net in base 3, because

1 times m-reduction [i] would yield (134, 206, 3801)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 934769 415751 380095 205436 900798 563004 567904 621654 780302 053745 746265 304613 552954 395746 284923 299089 > 3²⁰⁶ [i]