MinT - Best Known (166−73, 166, s)-Nets in Base 3

Best Known (166−73, 166, s)-Nets in Base 3

(166−73, 166, 80)-Net over F₃ — Constructive and digital

Digital (93, 166, 80)-net over F₃, using

4 times m-reduction [i] based on digital (93, 170, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 85, 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]

(166−73, 166, 122)-Net over F₃ — Digital

Digital (93, 166, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−73, 166, 1062)-Net in Base 3 — Upper bound on s

There is no (93, 166, 1063)-net in base 3, because

1 times m-reduction [i] would yield (93, 165, 1063)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 353577 137012 456136 212600 969513 401637 938968 827869 829423 988339 724731 149585 913913 > 3¹⁶⁵ [i]