MinT - Best Known (77, 77+41, s)-Nets in Base 3

Best Known (77, 77+41, s)-Nets in Base 3

(77, 77+41, 148)-Net over F₃ — Constructive and digital

Digital (77, 118, 148)-net over F₃, using

2 times m-reduction [i] based on digital (77, 120, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 60, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(77, 77+41, 182)-Net over F₃ — Digital

Digital (77, 118, 182)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+41, 2547)-Net in Base 3 — Upper bound on s

There is no (77, 118, 2548)-net in base 3, because

1 times m-reduction [i] would yield (77, 117, 2548)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 66 753730 001363 689792 043666 290130 703578 373324 828979 424961 > 3¹¹⁷ [i]