MinT - Best Known (207−53, 207, s)-Nets in Base 3

Best Known (207−53, 207, s)-Nets in Base 3

(207−53, 207, 288)-Net over F₃ — Constructive and digital

Digital (154, 207, 288)-net over F₃, using

t-expansion [i] based on 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]

(207−53, 207, 796)-Net over F₃ — Digital

Digital (154, 207, 796)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−53, 207, 31782)-Net in Base 3 — Upper bound on s

There is no (154, 207, 31783)-net in base 3, because

1 times m-reduction [i] would yield (154, 206, 31783)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 767418 803352 034395 381658 514356 198045 258769 920494 538270 622401 414540 907965 011999 344647 364638 022045 > 3²⁰⁶ [i]