MinT - Best Known (77, 77+48, s)-Nets in Base 3

Best Known (77, 77+48, s)-Nets in Base 3

(77, 77+48, 128)-Net over F₃ — Constructive and digital

Digital (77, 125, 128)-net over F₃, using

3 times m-reduction [i] based on digital (77, 128, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 64, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(77, 77+48, 141)-Net over F₃ — Digital

Digital (77, 125, 141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+48, 1474)-Net in Base 3 — Upper bound on s

There is no (77, 125, 1475)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 443315 803348 218834 502281 356735 116608 946620 103300 092170 878161 > 3¹²⁵ [i]