MinT - Best Known (206−57, 206, s)-Nets in Base 3

Best Known (206−57, 206, s)-Nets in Base 3

(206−57, 206, 288)-Net over F₃ — Constructive and digital

Digital (149, 206, 288)-net over F₃, using

1 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]

(206−57, 206, 596)-Net over F₃ — Digital

Digital (149, 206, 596)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−57, 206, 17559)-Net in Base 3 — Upper bound on s

There is no (149, 206, 17560)-net in base 3, because

1 times m-reduction [i] would yield (149, 205, 17560)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 625174 959631 301884 780819 697876 356190 603489 988310 640057 879113 976210 857558 714660 322798 072848 175297 > 3²⁰⁵ [i]