MinT - Best Known (117−42, 117, s)-Nets in Base 3

Best Known (117−42, 117, s)-Nets in Base 3

(117−42, 117, 128)-Net over F₃ — Constructive and digital

Digital (75, 117, 128)-net over F₃, using

7 times m-reduction [i] based on digital (75, 124, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 62, 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]

(117−42, 117, 163)-Net over F₃ — Digital

Digital (75, 117, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−42, 117, 1955)-Net in Base 3 — Upper bound on s

There is no (75, 117, 1956)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 67 098219 783312 912688 332992 392106 671509 413359 453416 497961 > 3¹¹⁷ [i]