MinT - Best Known (75, 75+46, s)-Nets in Base 3

Best Known (75, 75+46, s)-Nets in Base 3

(75, 75+46, 128)-Net over F₃ — Constructive and digital

Digital (75, 121, 128)-net over F₃, using

3 times m-reduction [i] based on digital (75, 124, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 62, 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]

(75, 75+46, 141)-Net over F₃ — Digital

Digital (75, 121, 141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+46, 1503)-Net in Base 3 — Upper bound on s

There is no (75, 121, 1504)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5436 527725 354235 941899 231784 784352 441939 626856 030988 156545 > 3¹²¹ [i]