MinT - Best Known (49, 49+27, s)-Nets in Base 3

Best Known (49, 49+27, s)-Nets in Base 3

(49, 49+27, 80)-Net over F₃ — Constructive and digital

Digital (49, 76, 80)-net over F₃, using

6 times m-reduction [i] based on digital (49, 82, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 41, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(49, 49+27, 121)-Net over F₃ — Digital

Digital (49, 76, 121)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+27, 1590)-Net in Base 3 — Upper bound on s

There is no (49, 76, 1591)-net in base 3, because

1 times m-reduction [i] would yield (49, 75, 1591)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 609344 529887 169869 915603 041830 962199 > 3⁷⁵ [i]