MinT - Best Known (117−37, 117, s)-Nets in Base 3

Best Known (117−37, 117, s)-Nets in Base 3

(117−37, 117, 148)-Net over F₃ — Constructive and digital

Digital (80, 117, 148)-net over F₃, using

9 times m-reduction [i] based on digital (80, 126, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 63, 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]

(117−37, 117, 240)-Net over F₃ — Digital

Digital (80, 117, 240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−37, 117, 4468)-Net in Base 3 — Upper bound on s

There is no (80, 117, 4469)-net in base 3, because

1 times m-reduction [i] would yield (80, 116, 4469)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22 206868 075956 428818 545548 075248 598172 040633 948945 474545 > 3¹¹⁶ [i]