MinT - Best Known (55, 55+39, s)-Nets in Base 3

Best Known (55, 55+39, s)-Nets in Base 3

(55, 55+39, 80)-Net over F₃ — Constructive and digital

Digital (55, 94, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 47, 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]

(55, 55+39, 91)-Net over F₃ — Digital

Digital (55, 94, 91)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+39, 839)-Net in Base 3 — Upper bound on s

There is no (55, 94, 840)-net in base 3, because

1 times m-reduction [i] would yield (55, 93, 840)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 236 567625 295989 764341 891882 453684 056208 384161 > 3⁹³ [i]