MinT - Best Known (137, 137+43, s)-Nets in Base 3

Best Known (137, 137+43, s)-Nets in Base 3

(137, 137+43, 464)-Net over F₃ — Constructive and digital

Digital (137, 180, 464)-net over F₃, using

trace code for nets [i] based on digital (2, 45, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(137, 137+43, 936)-Net over F₃ — Digital

Digital (137, 180, 936)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+43, 50603)-Net in Base 3 — Upper bound on s

There is no (137, 180, 50604)-net in base 3, because

1 times m-reduction [i] would yield (137, 179, 50604)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25 401599 017154 812949 974299 197327 973924 028382 866644 577887 827369 350411 102771 944381 726009 > 3¹⁷⁹ [i]