MinT - Best Known (166−71, 166, s)-Nets in Base 3

Best Known (166−71, 166, s)-Nets in Base 3

(166−71, 166, 80)-Net over F₃ — Constructive and digital

Digital (95, 166, 80)-net over F₃, using

8 times m-reduction [i] based on digital (95, 174, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 87, 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]

(166−71, 166, 132)-Net over F₃ — Digital

Digital (95, 166, 132)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−71, 166, 1200)-Net in Base 3 — Upper bound on s

There is no (95, 166, 1201)-net in base 3, because

1 times m-reduction [i] would yield (95, 165, 1201)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 388111 755414 880846 303895 342786 318874 582143 737444 805637 168926 043307 690467 154651 > 3¹⁶⁵ [i]