MinT - Best Known (171−77, 171, s)-Nets in Base 3

Best Known (171−77, 171, s)-Nets in Base 3

(171−77, 171, 80)-Net over F₃ — Constructive and digital

Digital (94, 171, 80)-net over F₃, using

1 times m-reduction [i] based on digital (94, 172, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 86, 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]

(171−77, 171, 117)-Net over F₃ — Digital

Digital (94, 171, 117)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−77, 171, 986)-Net in Base 3 — Upper bound on s

There is no (94, 171, 987)-net in base 3, because

1 times m-reduction [i] would yield (94, 170, 987)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1291 274643 999130 578562 777816 019054 060404 006608 091649 872324 014957 848336 356602 092877 > 3¹⁷⁰ [i]