MinT - Best Known (199−53, 199, s)-Nets in Base 3

Best Known (199−53, 199, s)-Nets in Base 3

(199−53, 199, 288)-Net over F₃ — Constructive and digital

Digital (146, 199, 288)-net over F₃, using

t-expansion [i] based on digital (145, 199, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (145, 201, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 67, 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]

(199−53, 199, 664)-Net over F₃ — Digital

Digital (146, 199, 664)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−53, 199, 22658)-Net in Base 3 — Upper bound on s

There is no (146, 199, 22659)-net in base 3, because

1 times m-reduction [i] would yield (146, 198, 22659)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29519 866558 668057 637095 243499 817982 958796 824126 318099 993676 774087 499326 447499 611342 946536 747445 > 3¹⁹⁸ [i]