MinT - Best Known (150, 150+71, s)-Nets in Base 3

Best Known (150, 150+71, s)-Nets in Base 3

(150, 150+71, 167)-Net over F₃ — Constructive and digital

Digital (150, 221, 167)-net over F₃, using

3¹ times duplication [i] based on digital (149, 220, 167)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 44, 19)-net over F₃, using
    - net from sequence [i] based on digital (9, 18)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using
        an explicitly constructive algebraic function field [i]
  2. digital (105, 176, 148)-net over F₃, using
    - trace code for nets [i] based on digital (17, 88, 74)-net over F₉, using
      - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
        a function field by GarcÃa and Quoos [i]

(150, 150+71, 390)-Net over F₃ — Digital

Digital (150, 221, 390)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+71, 6904)-Net in Base 3 — Upper bound on s

There is no (150, 221, 6905)-net in base 3, because

1 times m-reduction [i] would yield (150, 220, 6905)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 929 280859 297483 850566 142516 098750 645389 612818 980957 581990 539416 125043 556575 042352 578020 037002 924409 874235 > 3²²⁰ [i]