MinT - Best Known (207−55, 207, s)-Nets in Base 3

Best Known (207−55, 207, s)-Nets in Base 3

(207−55, 207, 288)-Net over F₃ — Constructive and digital

Digital (152, 207, 288)-net over F₃, using

t-expansion [i] based on digital (151, 207, 288)-net over F₃, using
- 3 times m-reduction [i] based on digital (151, 210, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 70, 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]

(207−55, 207, 693)-Net over F₃ — Digital

Digital (152, 207, 693)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−55, 207, 23831)-Net in Base 3 — Upper bound on s

There is no (152, 207, 23832)-net in base 3, because

1 times m-reduction [i] would yield (152, 206, 23832)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 725020 153798 390937 079222 327537 040757 031178 578698 648125 007289 718574 091473 597743 697599 674601 720289 > 3²⁰⁶ [i]