MinT - Best Known (78, 78+37, s)-Nets in Base 3

Best Known (78, 78+37, s)-Nets in Base 3

(78, 78+37, 148)-Net over F₃ — Constructive and digital

Digital (78, 115, 148)-net over F₃, using

7 times m-reduction [i] based on digital (78, 122, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 61, 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]

(78, 78+37, 224)-Net over F₃ — Digital

Digital (78, 115, 224)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+37, 3953)-Net in Base 3 — Upper bound on s

There is no (78, 115, 3954)-net in base 3, because

1 times m-reduction [i] would yield (78, 114, 3954)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 473533 032873 747426 238317 513329 462736 737562 118724 972245 > 3¹¹⁴ [i]