MinT - Best Known (39, 39+25, s)-Nets in Base 3

Best Known (39, 39+25, s)-Nets in Base 3

(39, 39+25, 72)-Net over F₃ — Constructive and digital

Digital (39, 64, 72)-net over F₃, using

trace code for nets [i] based on digital (7, 32, 36)-net over F₉, using
- net from sequence [i] based on digital (7, 35)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
    - a function field by SÃ©mirat [i]

(39, 39+25, 82)-Net over F₃ — Digital

Digital (39, 64, 82)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+25, 834)-Net in Base 3 — Upper bound on s

There is no (39, 64, 835)-net in base 3, because

1 times m-reduction [i] would yield (39, 63, 835)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 156500 814342 116211 412613 128521 > 3⁶³ [i]