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

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

(77, 77+29, 228)-Net over F₃ — Constructive and digital

Digital (77, 106, 228)-net over F₃, using

3¹ times duplication [i] based on digital (76, 105, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 35, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(77, 77+29, 369)-Net over F₃ — Digital

Digital (77, 106, 369)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+29, 11437)-Net in Base 3 — Upper bound on s

There is no (77, 106, 11438)-net in base 3, because

1 times m-reduction [i] would yield (77, 105, 11438)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 125 337587 821823 255508 016929 392556 768443 971074 917973 > 3¹⁰⁵ [i]