MinT - Best Known (39−15, 39, s)-Nets in Base 3

Best Known (39−15, 39, s)-Nets in Base 3

(39−15, 39, 60)-Net over F₃ — Constructive and digital

Digital (24, 39, 60)-net over F₃, using

1 times m-reduction [i] based on digital (24, 40, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 20, 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]

(39−15, 39, 62)-Net over F₃ — Digital

Digital (24, 39, 62)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(39−15, 39, 651)-Net in Base 3 — Upper bound on s

There is no (24, 39, 652)-net in base 3, because

1 times m-reduction [i] would yield (24, 38, 652)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 363157 360959 491153 > 3³⁸ [i]