MinT - Best Known (197−51, 197, s)-Nets in Base 3

Best Known (197−51, 197, s)-Nets in Base 3

(197−51, 197, 288)-Net over F₃ — Constructive and digital

Digital (146, 197, 288)-net over F₃, using

t-expansion [i] based on digital (145, 197, 288)-net over F₃, using
- 4 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]

(197−51, 197, 733)-Net over F₃ — Digital

Digital (146, 197, 733)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−51, 197, 27979)-Net in Base 3 — Upper bound on s

There is no (146, 197, 27980)-net in base 3, because

1 times m-reduction [i] would yield (146, 196, 27980)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3279 414526 630321 425758 261315 785899 865702 506471 933339 387983 978211 597048 681624 588842 782377 099801 > 3¹⁹⁶ [i]