MinT - Best Known (190−78, 190, s)-Nets in Base 3

Best Known (190−78, 190, s)-Nets in Base 3

(190−78, 190, 148)-Net over F₃ — Constructive and digital

Digital (112, 190, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 95, 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]

(190−78, 190, 166)-Net over F₃ — Digital

Digital (112, 190, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−78, 190, 1586)-Net in Base 3 — Upper bound on s

There is no (112, 190, 1587)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 520221 757898 075193 413346 598369 096082 081273 102627 898037 403732 741766 247168 493616 017537 522051 > 3¹⁹⁰ [i]