MinT - Best Known (223−90, 223, s)-Nets in Base 3

Best Known (223−90, 223, s)-Nets in Base 3

(223−90, 223, 148)-Net over F₃ — Constructive and digital

Digital (133, 223, 148)-net over F₃, using

9 times m-reduction [i] based on digital (133, 232, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 116, 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]

(223−90, 223, 200)-Net over F₃ — Digital

Digital (133, 223, 200)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−90, 223, 1995)-Net in Base 3 — Upper bound on s

There is no (133, 223, 1996)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25284 288277 739176 541855 893785 022305 048091 685925 776249 475895 423995 054528 015737 232987 282999 596758 548585 575801 > 3²²³ [i]