MinT - Best Known (58, 58+46, s)-Nets in Base 3

Best Known (58, 58+46, s)-Nets in Base 3

(58, 58+46, 68)-Net over F₃ — Constructive and digital

Digital (58, 104, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 52, 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]

(58, 58+46, 82)-Net over F₃ — Digital

Digital (58, 104, 82)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+46, 655)-Net in Base 3 — Upper bound on s

There is no (58, 104, 656)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 42 887125 665792 402595 279246 270387 340731 336188 448449 > 3¹⁰⁴ [i]