MinT - Best Known (59, 59+43, s)-Nets in Base 3

Best Known (59, 59+43, s)-Nets in Base 3

(59, 59+43, 80)-Net over F₃ — Constructive and digital

Digital (59, 102, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 51, 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]

(59, 59+43, 93)-Net over F₃ — Digital

Digital (59, 102, 93)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+43, 835)-Net in Base 3 — Upper bound on s

There is no (59, 102, 836)-net in base 3, because

1 times m-reduction [i] would yield (59, 101, 836)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 579073 238134 390936 247469 866892 285338 767117 212777 > 3¹⁰¹ [i]