MinT - Best Known (63−27, 63, s)-Nets in Base 3

Best Known (63−27, 63, s)-Nets in Base 3

(63−27, 63, 60)-Net over F₃ — Constructive and digital

Digital (36, 63, 60)-net over F₃, using

1 times m-reduction [i] based on digital (36, 64, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 32, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]

(63−27, 63, 62)-Net over F₃ — Digital

Digital (36, 63, 62)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−27, 63, 522)-Net in Base 3 — Upper bound on s

There is no (36, 63, 523)-net in base 3, because

1 times m-reduction [i] would yield (36, 62, 523)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 390578 422302 415022 384017 643391 > 3⁶² [i]