MinT - Best Known (167, 167+69, s)-Nets in Base 3

Best Known (167, 167+69, s)-Nets in Base 3

(167, 167+69, 264)-Net over F₃ — Constructive and digital

Digital (167, 236, 264)-net over F₃, using

1 times m-reduction [i] based on digital (167, 237, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 79, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(167, 167+69, 556)-Net over F₃ — Digital

Digital (167, 236, 556)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+69, 13400)-Net in Base 3 — Upper bound on s

There is no (167, 236, 13401)-net in base 3, because

1 times m-reduction [i] would yield (167, 235, 13401)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13315 215624 823337 206204 724453 283946 178370 591659 116477 808709 156957 085137 050910 989248 248061 795814 177833 199424 001145 > 3²³⁵ [i]