MinT - Best Known (156−57, 156, s)-Nets in Base 3

Best Known (156−57, 156, s)-Nets in Base 3

(156−57, 156, 148)-Net over F₃ — Constructive and digital

Digital (99, 156, 148)-net over F₃, using

8 times m-reduction [i] based on digital (99, 164, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 82, 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]

(156−57, 156, 196)-Net over F₃ — Digital

Digital (99, 156, 196)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−57, 156, 2445)-Net in Base 3 — Upper bound on s

There is no (99, 156, 2446)-net in base 3, because

1 times m-reduction [i] would yield (99, 155, 2446)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 90 533270 989215 003202 779950 596802 346147 268387 106373 619248 262082 656050 007929 > 3¹⁵⁵ [i]