MinT - Best Known (137, 200, s)-Nets in Base 3

Best Known (137, 200, s)-Nets in Base 3

(137, 200, 167)-Net over F₃ — Constructive and digital

Digital (137, 200, 167)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (9, 40, 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 (97, 160, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 80, 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]

(137, 200, 380)-Net over F₃ — Digital

Digital (137, 200, 380)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 200, 7144)-Net in Base 3 — Upper bound on s

There is no (137, 200, 7145)-net in base 3, because

1 times m-reduction [i] would yield (137, 199, 7145)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88761 354573 412865 305019 065885 198033 635424 867641 257684 601325 253770 203577 579043 794407 179398 184907 > 3¹⁹⁹ [i]