MinT - Best Known (60, 60+33, s)-Nets in Base 3

Best Known (60, 60+33, s)-Nets in Base 3

(60, 60+33, 128)-Net over F₃ — Constructive and digital

Digital (60, 93, 128)-net over F₃, using

1 times m-reduction [i] based on digital (60, 94, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 47, 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]

(60, 60+33, 142)-Net over F₃ — Digital

Digital (60, 93, 142)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+33, 1868)-Net in Base 3 — Upper bound on s

There is no (60, 93, 1869)-net in base 3, because

1 times m-reduction [i] would yield (60, 92, 1869)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 79 214115 164092 797379 459173 099180 244319 536065 > 3⁹² [i]