MinT - Best Known (60, 60+44, s)-Nets in Base 3

Best Known (60, 60+44, s)-Nets in Base 3

(60, 60+44, 80)-Net over F₃ — Constructive and digital

Digital (60, 104, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 52, 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]

(60, 60+44, 93)-Net over F₃ — Digital

Digital (60, 104, 93)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+44, 794)-Net in Base 3 — Upper bound on s

There is no (60, 104, 795)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 42 874246 699387 571067 028480 272503 425947 475940 682093 > 3¹⁰⁴ [i]