MinT - Best Known (77, 130, s)-Nets in Base 3

Best Known (77, 130, s)-Nets in Base 3

(77, 130, 80)-Net over F₃ — Constructive and digital

Digital (77, 130, 80)-net over F₃, using

8 times m-reduction [i] based on digital (77, 138, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 69, 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, 130, 123)-Net over F₃ — Digital

Digital (77, 130, 123)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 130, 1203)-Net in Base 3 — Upper bound on s

There is no (77, 130, 1204)-net in base 3, because

1 times m-reduction [i] would yield (77, 129, 1204)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35 652879 318244 257073 641584 118854 103400 045604 574939 891061 228761 > 3¹²⁹ [i]