MinT - Best Known (157, 157+55, s)-Nets in Base 3

Best Known (157, 157+55, s)-Nets in Base 3

(157, 157+55, 288)-Net over F₃ — Constructive and digital

Digital (157, 212, 288)-net over F₃, using

7 times m-reduction [i] based on digital (157, 219, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 73, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(157, 157+55, 772)-Net over F₃ — Digital

Digital (157, 212, 772)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+55, 29214)-Net in Base 3 — Upper bound on s

There is no (157, 212, 29215)-net in base 3, because

1 times m-reduction [i] would yield (157, 211, 29215)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47077 515249 447444 264069 291569 198503 503121 093205 925535 706746 657447 583817 182858 841310 454309 775886 234699 > 3²¹¹ [i]