MinT - Best Known (149, 149+54, s)-Nets in Base 3

Best Known (149, 149+54, s)-Nets in Base 3

(149, 149+54, 288)-Net over F₃ — Constructive and digital

Digital (149, 203, 288)-net over F₃, using

4 times m-reduction [i] based on digital (149, 207, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 69, 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]

(149, 149+54, 679)-Net over F₃ — Digital

Digital (149, 203, 679)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+54, 21090)-Net in Base 3 — Upper bound on s

There is no (149, 203, 21091)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 180702 844335 760449 165005 950755 294921 953875 680882 932278 259101 872816 637782 850491 876996 235073 552251 > 3²⁰³ [i]