MinT - Best Known (207−54, 207, s)-Nets in Base 3

Best Known (207−54, 207, s)-Nets in Base 3

(207−54, 207, 288)-Net over F₃ — Constructive and digital

Digital (153, 207, 288)-net over F₃, using

6 times m-reduction [i] based on digital (153, 213, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 71, 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]

(207−54, 207, 742)-Net over F₃ — Digital

Digital (153, 207, 742)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−54, 207, 24822)-Net in Base 3 — Upper bound on s

There is no (153, 207, 24823)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 581 297153 342963 054178 530709 054759 123419 950905 644964 790728 698339 201932 131501 003364 645305 009699 947819 > 3²⁰⁷ [i]