MinT - Best Known (77, 77+62, s)-Nets in Base 3

Best Known (77, 77+62, s)-Nets in Base 3

(77, 77+62, 72)-Net over F₃ — Constructive and digital

Digital (77, 139, 72)-net over F₃, using

1 times m-reduction [i] based on digital (77, 140, 72)-net over F₃, using
- trace code for nets [i] based on digital (7, 70, 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]

(77, 77+62, 101)-Net over F₃ — Digital

Digital (77, 139, 101)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+62, 825)-Net in Base 3 — Upper bound on s

There is no (77, 139, 826)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 110844 771087 514187 479680 340722 716413 904140 806551 009445 043420 653721 > 3¹³⁹ [i]