MinT - Best Known (50, 50+29, s)-Nets in Base 3

Best Known (50, 50+29, s)-Nets in Base 3

(50, 50+29, 80)-Net over F₃ — Constructive and digital

Digital (50, 79, 80)-net over F₃, using

5 times m-reduction [i] based on digital (50, 84, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 42, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(50, 50+29, 113)-Net over F₃ — Digital

Digital (50, 79, 113)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+29, 1362)-Net in Base 3 — Upper bound on s

There is no (50, 79, 1363)-net in base 3, because

1 times m-reduction [i] would yield (50, 78, 1363)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 467769 244084 603986 600010 963887 146093 > 3⁷⁸ [i]