MinT - Best Known (167, 167+51, s)-Nets in Base 3

Best Known (167, 167+51, s)-Nets in Base 3

(167, 167+51, 464)-Net over F₃ — Constructive and digital

Digital (167, 218, 464)-net over F₃, using

2 times m-reduction [i] based on digital (167, 220, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 55, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(167, 167+51, 1196)-Net over F₃ — Digital

Digital (167, 218, 1196)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+51, 70446)-Net in Base 3 — Upper bound on s

There is no (167, 218, 70447)-net in base 3, because

1 times m-reduction [i] would yield (167, 217, 70447)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 311646 204748 171031 864431 555448 810465 231380 607499 691658 032826 345098 711930 798399 463784 282925 362158 791727 > 3²¹⁷ [i]