MinT - Best Known (216−87, 216, s)-Nets in Base 3

Best Known (216−87, 216, s)-Nets in Base 3

(216−87, 216, 148)-Net over F₃ — Constructive and digital

Digital (129, 216, 148)-net over F₃, using

8 times m-reduction [i] based on digital (129, 224, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 112, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(216−87, 216, 196)-Net over F₃ — Digital

Digital (129, 216, 196)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−87, 216, 2009)-Net in Base 3 — Upper bound on s

There is no (129, 216, 2010)-net in base 3, because

1 times m-reduction [i] would yield (129, 215, 2010)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 872701 989153 353939 279562 248011 172398 526921 253228 659267 849093 824268 658626 813630 638695 380327 187175 600353 > 3²¹⁵ [i]