MinT - Best Known (116−37, 116, s)-Nets in Base 3

Best Known (116−37, 116, s)-Nets in Base 3

(116−37, 116, 148)-Net over F₃ — Constructive and digital

Digital (79, 116, 148)-net over F₃, using

8 times m-reduction [i] based on digital (79, 124, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 62, 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]

(116−37, 116, 232)-Net over F₃ — Digital

Digital (79, 116, 232)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−37, 116, 4203)-Net in Base 3 — Upper bound on s

There is no (79, 116, 4204)-net in base 3, because

1 times m-reduction [i] would yield (79, 115, 4204)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 422412 276831 825246 477202 031114 715463 186571 997281 624745 > 3¹¹⁵ [i]