MinT - Best Known (74, 74+37, s)-Nets in Base 3

Best Known (74, 74+37, s)-Nets in Base 3

(74, 74+37, 148)-Net over F₃ — Constructive and digital

Digital (74, 111, 148)-net over F₃, using

3 times m-reduction [i] based on digital (74, 114, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 57, 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]

(74, 74+37, 195)-Net over F₃ — Digital

Digital (74, 111, 195)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+37, 3093)-Net in Base 3 — Upper bound on s

There is no (74, 111, 3094)-net in base 3, because

1 times m-reduction [i] would yield (74, 110, 3094)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30588 078017 112954 348894 799634 389628 128131 920233 128045 > 3¹¹⁰ [i]