MinT - Best Known (157, 157+59, s)-Nets in Base 3

Best Known (157, 157+59, s)-Nets in Base 3

(157, 157+59, 288)-Net over F₃ — Constructive and digital

Digital (157, 216, 288)-net over F₃, using

3 times m-reduction [i] based on digital (157, 219, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 73, 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]

(157, 157+59, 650)-Net over F₃ — Digital

Digital (157, 216, 650)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 157+59, 20079)-Net in Base 3 — Upper bound on s

There is no (157, 216, 20080)-net in base 3, because

1 times m-reduction [i] would yield (157, 215, 20080)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 813564 327889 436714 720074 727785 009959 691393 588462 422749 514614 093246 988008 959429 317371 643631 760290 977249 > 3²¹⁵ [i]