MinT - Best Known (77−29, 77, s)-Nets in Base 3

Best Known (77−29, 77, s)-Nets in Base 3

(77−29, 77, 80)-Net over F₃ — Constructive and digital

Digital (48, 77, 80)-net over F₃, using

3 times m-reduction [i] based on digital (48, 80, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 40, 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]

(77−29, 77, 104)-Net over F₃ — Digital

Digital (48, 77, 104)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−29, 77, 1162)-Net in Base 3 — Upper bound on s

There is no (48, 77, 1163)-net in base 3, because

1 times m-reduction [i] would yield (48, 76, 1163)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 827953 437149 352303 847814 134463 242013 > 3⁷⁶ [i]