MinT - Best Known (61, 61+45, s)-Nets in Base 3

Best Known (61, 61+45, s)-Nets in Base 3

(61, 61+45, 80)-Net over F₃ — Constructive and digital

Digital (61, 106, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 53, 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]

(61, 61+45, 93)-Net over F₃ — Digital

Digital (61, 106, 93)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+45, 835)-Net in Base 3 — Upper bound on s

There is no (61, 106, 836)-net in base 3, because

1 times m-reduction [i] would yield (61, 105, 836)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 126 056339 828586 193732 865172 336524 559431 138265 338201 > 3¹⁰⁵ [i]