MinT - Best Known (49, 86, s)-Nets in Base 3

Best Known (49, 86, s)-Nets in Base 3

(49, 86, 68)-Net over F₃ — Constructive and digital

Digital (49, 86, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 43, 34)-net over F₉, using
- net from sequence [i] based on digital (6, 33)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(49, 86, 77)-Net over F₃ — Digital

Digital (49, 86, 77)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 86, 659)-Net in Base 3 — Upper bound on s

There is no (49, 86, 660)-net in base 3, because

1 times m-reduction [i] would yield (49, 85, 660)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 36847 833458 782375 857746 338005 216894 755481 > 3⁸⁵ [i]