MinT - Best Known (90, 90+71, s)-Nets in Base 3

Best Known (90, 90+71, s)-Nets in Base 3

(90, 90+71, 80)-Net over F₃ — Constructive and digital

Digital (90, 161, 80)-net over F₃, using

3 times m-reduction [i] based on digital (90, 164, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 82, 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]

(90, 90+71, 118)-Net over F₃ — Digital

Digital (90, 161, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+71, 1021)-Net in Base 3 — Upper bound on s

There is no (90, 161, 1022)-net in base 3, because

1 times m-reduction [i] would yield (90, 160, 1022)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22417 982764 384259 950189 006037 254037 049735 078796 558439 038529 935804 744914 974913 > 3¹⁶⁰ [i]