MinT - Best Known (125, 125+83, s)-Nets in Base 3

Best Known (125, 125+83, s)-Nets in Base 3

(125, 125+83, 148)-Net over F₃ — Constructive and digital

Digital (125, 208, 148)-net over F₃, using

8 times m-reduction [i] based on digital (125, 216, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 108, 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]

(125, 125+83, 195)-Net over F₃ — Digital

Digital (125, 208, 195)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 125+83, 2028)-Net in Base 3 — Upper bound on s

There is no (125, 208, 2029)-net in base 3, because

1 times m-reduction [i] would yield (125, 207, 2029)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 582 728810 004438 191900 660755 893288 987890 509767 968171 655493 210327 237255 308594 893966 781339 637674 916155 > 3²⁰⁷ [i]