MinT - Best Known (115, 115+81, s)-Nets in Base 3

Best Known (115, 115+81, s)-Nets in Base 3

(115, 115+81, 148)-Net over F₃ — Constructive and digital

Digital (115, 196, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 98, 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]

(115, 115+81, 167)-Net over F₃ — Digital

Digital (115, 196, 167)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+81, 1630)-Net in Base 3 — Upper bound on s

There is no (115, 196, 1631)-net in base 3, because

1 times m-reduction [i] would yield (115, 195, 1631)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1094 989822 088056 525584 448174 622819 052664 788879 106551 935771 530546 178300 211295 630292 139266 801073 > 3¹⁹⁵ [i]