MinT - Best Known (117, 117+85, s)-Nets in Base 3

Best Known (117, 117+85, s)-Nets in Base 3

(117, 117+85, 128)-Net over F₃ — Constructive and digital

Digital (117, 202, 128)-net over F₃, using

6 times m-reduction [i] based on digital (117, 208, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 104, 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, 117+85, 164)-Net over F₃ — Digital

Digital (117, 202, 164)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+85, 1544)-Net in Base 3 — Upper bound on s

There is no (117, 202, 1545)-net in base 3, because

1 times m-reduction [i] would yield (117, 201, 1545)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 810825 325726 468069 109634 328884 885064 360206 568424 640135 607663 559842 653426 854727 794170 046063 489145 > 3²⁰¹ [i]