MinT - Best Known (176, 176+69, s)-Nets in Base 3

Best Known (176, 176+69, s)-Nets in Base 3

(176, 176+69, 288)-Net over F₃ — Constructive and digital

Digital (176, 245, 288)-net over F₃, using

t-expansion [i] based on digital (175, 245, 288)-net over F₃, using
- 1 times m-reduction [i] based on digital (175, 246, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 82, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(176, 176+69, 652)-Net over F₃ — Digital

Digital (176, 245, 652)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 176+69, 17934)-Net in Base 3 — Upper bound on s

There is no (176, 245, 17935)-net in base 3, because

1 times m-reduction [i] would yield (176, 244, 17935)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 261 960519 341114 114581 784997 576395 534632 190983 895022 636892 212264 993031 489188 816765 573562 555170 534010 796718 135417 935325 > 3²⁴⁴ [i]