MinT - Best Known (175−63, 175, s)-Nets in Base 3

Best Known (175−63, 175, s)-Nets in Base 3

(175−63, 175, 156)-Net over F₃ — Constructive and digital

Digital (112, 175, 156)-net over F₃, using

5 times m-reduction [i] based on digital (112, 180, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 90, 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]

(175−63, 175, 225)-Net over F₃ — Digital

Digital (112, 175, 225)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−63, 175, 2927)-Net in Base 3 — Upper bound on s

There is no (112, 175, 2928)-net in base 3, because

1 times m-reduction [i] would yield (112, 174, 2928)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104600 159998 197246 099603 363732 085824 002384 585398 162222 261988 684374 060495 006620 236097 > 3¹⁷⁴ [i]