MinT - Best Known (52, 52+43, s)-Nets in Base 3

Best Known (52, 52+43, s)-Nets in Base 3

(52, 52+43, 60)-Net over F₃ — Constructive and digital

Digital (52, 95, 60)-net over F₃, using

1 times m-reduction [i] based on digital (52, 96, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 48, 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]

(52, 52+43, 72)-Net over F₃ — Digital

Digital (52, 95, 72)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+43, 572)-Net in Base 3 — Upper bound on s

There is no (52, 95, 573)-net in base 3, because

1 times m-reduction [i] would yield (52, 94, 573)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 709 005501 364568 458380 779471 214898 360893 161547 > 3⁹⁴ [i]