MinT - Best Known (99, 155, s)-Nets in Base 3

Best Known (99, 155, s)-Nets in Base 3

(99, 155, 148)-Net over F₃ — Constructive and digital

Digital (99, 155, 148)-net over F₃, using

9 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]

(99, 155, 201)-Net over F₃ — Digital

Digital (99, 155, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 155, 2445)-Net in Base 3 — Upper bound on s

There is no (99, 155, 2446)-net in base 3, because

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]