MinT - Best Known (117−43, 117, s)-Nets in Base 3

Best Known (117−43, 117, s)-Nets in Base 3

(117−43, 117, 128)-Net over F₃ — Constructive and digital

Digital (74, 117, 128)-net over F₃, using

5 times m-reduction [i] based on digital (74, 122, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 61, 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]

(117−43, 117, 152)-Net over F₃ — Digital

Digital (74, 117, 152)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−43, 117, 1854)-Net in Base 3 — Upper bound on s

There is no (74, 117, 1855)-net in base 3, because

1 times m-reduction [i] would yield (74, 116, 1855)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22 299300 022433 106392 138409 119576 297992 671509 439012 578391 > 3¹¹⁶ [i]