MinT - Best Known (216−89, 216, s)-Nets in Base 3

Best Known (216−89, 216, s)-Nets in Base 3

(216−89, 216, 148)-Net over F₃ — Constructive and digital

Digital (127, 216, 148)-net over F₃, using

4 times m-reduction [i] based on digital (127, 220, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 110, 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]

(216−89, 216, 184)-Net over F₃ — Digital

Digital (127, 216, 184)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−89, 216, 1807)-Net in Base 3 — Upper bound on s

There is no (127, 216, 1808)-net in base 3, because

1 times m-reduction [i] would yield (127, 215, 1808)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 867377 649847 326233 401083 828067 425433 618256 474139 172008 107687 759130 026669 585801 788387 583626 031466 219393 > 3²¹⁵ [i]