MinT - Best Known (89, 89+56, s)-Nets in Base 3

Best Known (89, 89+56, s)-Nets in Base 3

(89, 89+56, 128)-Net over F₃ — Constructive and digital

Digital (89, 145, 128)-net over F₃, using

7 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, 89+56, 157)-Net over F₃ — Digital

Digital (89, 145, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+56, 1642)-Net in Base 3 — Upper bound on s

There is no (89, 145, 1643)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1524 176751 280027 701180 941115 788836 003153 276323 226196 314208 597689 558953 > 3¹⁴⁵ [i]