MinT - Best Known (150−69, 150, s)-Nets in Base 3

Best Known (150−69, 150, s)-Nets in Base 3

(150−69, 150, 68)-Net over F₃ — Constructive and digital

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]

(150−69, 150, 99)-Net over F₃ — Digital

Digital (81, 150, 99)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−69, 150, 801)-Net in Base 3 — Upper bound on s

There is no (81, 150, 802)-net in base 3, because

1 times m-reduction [i] would yield (81, 149, 802)-net in base 3, but
- 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]