MinT - Best Known (70, 110, s)-Nets in Base 3

Best Known (70, 110, s)-Nets in Base 3

(70, 110, 128)-Net over F₃ — Constructive and digital

Digital (70, 110, 128)-net over F₃, using

4 times m-reduction [i] based on digital (70, 114, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 57, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(70, 110, 150)-Net over F₃ — Digital

Digital (70, 110, 150)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 110, 1728)-Net in Base 3 — Upper bound on s

There is no (70, 110, 1729)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30714 161108 222217 976199 318504 026041 189523 617526 436241 > 3¹¹⁰ [i]