MinT - Best Known (167, 167+68, s)-Nets in Base 3

Best Known (167, 167+68, s)-Nets in Base 3

(167, 167+68, 282)-Net over F₃ — Constructive and digital

Digital (167, 235, 282)-net over F₃, using

3¹ times duplication [i] based on digital (166, 234, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 78, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(167, 167+68, 574)-Net over F₃ — Digital

Digital (167, 235, 574)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+68, 13400)-Net in Base 3 — Upper bound on s

There is no (167, 235, 13401)-net in base 3, because

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]