MinT - Best Known (86, 86+65, s)-Nets in Base 3

Best Known (86, 86+65, s)-Nets in Base 3

(86, 86+65, 80)-Net over F₃ — Constructive and digital

Digital (86, 151, 80)-net over F₃, using

5 times m-reduction [i] based on digital (86, 156, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 78, 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]

(86, 86+65, 120)-Net over F₃ — Digital

Digital (86, 151, 120)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+65, 1071)-Net in Base 3 — Upper bound on s

There is no (86, 151, 1072)-net in base 3, because

1 times m-reduction [i] would yield (86, 150, 1072)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 377436 127702 772391 191525 273224 480186 629833 445339 982787 887590 272325 748737 > 3¹⁵⁰ [i]