MinT - Best Known (99, 99+77, s)-Nets in Base 3

Best Known (99, 99+77, s)-Nets in Base 3

(99, 99+77, 80)-Net over F₃ — Constructive and digital

Digital (99, 176, 80)-net over F₃, using

6 times m-reduction [i] based on digital (99, 182, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 91, 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]

(99, 99+77, 130)-Net over F₃ — Digital

Digital (99, 176, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+77, 1146)-Net in Base 3 — Upper bound on s

There is no (99, 176, 1147)-net in base 3, because

1 times m-reduction [i] would yield (99, 175, 1147)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 322226 024556 531298 671666 277736 421179 006931 066128 393798 464125 458981 268872 343913 957773 > 3¹⁷⁵ [i]