MinT - Best Known (81, 81+68, s)-Nets in Base 3

Best Known (81, 81+68, s)-Nets in Base 3

(81, 81+68, 68)-Net over F₃ — Constructive and digital

Digital (81, 149, 68)-net over F₃, using

1 times m-reduction [i] based on digital (81, 150, 68)-net over F₃, using
- trace code for nets [i] based on digital (6, 75, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(81, 81+68, 101)-Net over F₃ — Digital

Digital (81, 149, 101)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+68, 801)-Net in Base 3 — Upper bound on s

There is no (81, 149, 802)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 126277 486717 563275 260947 300928 782861 057058 597940 592951 260308 178852 357397 > 3¹⁴⁹ [i]