MinT - Best Known (59, 59+45, s)-Nets in Base 3

Best Known (59, 59+45, s)-Nets in Base 3

(59, 59+45, 72)-Net over F₃ — Constructive and digital

Digital (59, 104, 72)-net over F₃, using

trace code for nets [i] based on digital (7, 52, 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]

(59, 59+45, 87)-Net over F₃ — Digital

Digital (59, 104, 87)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+45, 754)-Net in Base 3 — Upper bound on s

There is no (59, 104, 755)-net in base 3, because

1 times m-reduction [i] would yield (59, 103, 755)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 14 190108 221438 755408 258899 439847 001090 414608 676701 > 3¹⁰³ [i]