MinT - Best Known (112−37, 112, s)-Nets in Base 3

Best Known (112−37, 112, s)-Nets in Base 3

(112−37, 112, 148)-Net over F₃ — Constructive and digital

Digital (75, 112, 148)-net over F₃, using

4 times m-reduction [i] based on digital (75, 116, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 58, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(112−37, 112, 202)-Net over F₃ — Digital

Digital (75, 112, 202)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−37, 112, 3288)-Net in Base 3 — Upper bound on s

There is no (75, 112, 3289)-net in base 3, because

1 times m-reduction [i] would yield (75, 111, 3289)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 91356 820916 402068 069810 184889 804632 909092 053872 789305 > 3¹¹¹ [i]