MinT - Best Known (49−17, 49, s)-Nets in Base 3

Best Known (49−17, 49, s)-Nets in Base 3

(49−17, 49, 72)-Net over F₃ — Constructive and digital

Digital (32, 49, 72)-net over F₃, using

1 times m-reduction [i] based on digital (32, 50, 72)-net over F₃, using
- trace code for nets [i] based on digital (7, 25, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]

(49−17, 49, 97)-Net over F₃ — Digital

Digital (32, 49, 97)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(49−17, 49, 1364)-Net in Base 3 — Upper bound on s

There is no (32, 49, 1365)-net in base 3, because

1 times m-reduction [i] would yield (32, 48, 1365)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 79941 962402 454584 902497 > 3⁴⁸ [i]