MinT - Best Known (202−73, 202, s)-Nets in Base 3

Best Known (202−73, 202, s)-Nets in Base 3

(202−73, 202, 156)-Net over F₃ — Constructive and digital

Digital (129, 202, 156)-net over F₃, using

12 times m-reduction [i] based on digital (129, 214, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 107, 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]

(202−73, 202, 252)-Net over F₃ — Digital

Digital (129, 202, 252)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−73, 202, 3257)-Net in Base 3 — Upper bound on s

There is no (129, 202, 3258)-net in base 3, because

1 times m-reduction [i] would yield (129, 201, 3258)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 797015 017100 385331 989356 277994 237462 216756 831480 105856 145074 014176 016117 667756 895666 924210 984681 > 3²⁰¹ [i]