MinT - Best Known (112−39, 112, s)-Nets in Base 3

Best Known (112−39, 112, s)-Nets in Base 3

(112−39, 112, 148)-Net over F₃ — Constructive and digital

Digital (73, 112, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 56, 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]

(112−39, 112, 173)-Net over F₃ — Digital

Digital (73, 112, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−39, 112, 2411)-Net in Base 3 — Upper bound on s

There is no (73, 112, 2412)-net in base 3, because

1 times m-reduction [i] would yield (73, 111, 2412)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 91726 094830 680753 571715 990059 145273 464488 859666 480977 > 3¹¹¹ [i]