MinT - Best Known (250−110, 250, s)-Nets in Base 3

Best Known (250−110, 250, s)-Nets in Base 3

(250−110, 250, 128)-Net over F₃ — Constructive and digital

Digital (140, 250, 128)-net over F₃, using

t-expansion [i] based on digital (138, 250, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 125, 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]

(250−110, 250, 174)-Net over F₃ — Digital

Digital (140, 250, 174)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−110, 250, 1519)-Net in Base 3 — Upper bound on s

There is no (140, 250, 1520)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 192351 098855 709173 568329 696006 753356 066348 691279 451375 595098 513233 324817 745574 167327 663843 830138 147663 111218 019212 388161 > 3²⁵⁰ [i]