MinT - Best Known (195−53, 195, s)-Nets in Base 3

Best Known (195−53, 195, s)-Nets in Base 3

(195−53, 195, 288)-Net over F₃ — Constructive and digital

Digital (142, 195, 288)-net over F₃, using

t-expansion [i] based on digital (141, 195, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 65, 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]

(195−53, 195, 607)-Net over F₃ — Digital

Digital (142, 195, 607)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−53, 195, 19131)-Net in Base 3 — Upper bound on s

There is no (142, 195, 19132)-net in base 3, because

1 times m-reduction [i] would yield (142, 194, 19132)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 722194 214410 782686 657994 885539 305800 966960 395249 582965 420433 748504 983170 401228 927370 276745 > 3¹⁹⁴ [i]