MinT - Best Known (89, 149, s)-Nets in Base 3

Best Known (89, 149, s)-Nets in Base 3

(89, 149, 128)-Net over F₃ — Constructive and digital

Digital (89, 149, 128)-net over F₃, using

3 times m-reduction [i] based on digital (89, 152, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 76, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(89, 149, 143)-Net over F₃ — Digital

Digital (89, 149, 143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 149, 1381)-Net in Base 3 — Upper bound on s

There is no (89, 149, 1382)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 124541 710944 349798 911715 584115 656373 024044 008259 385003 764418 124127 799365 > 3¹⁴⁹ [i]