MinT - Best Known (174−101, 174, s)-Nets in Base 3

Best Known (174−101, 174, s)-Nets in Base 3

(174−101, 174, 48)-Net over F₃ — Constructive and digital

Digital (73, 174, 48)-net over F₃, using

t-expansion [i] based on digital (45, 174, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(174−101, 174, 84)-Net over F₃ — Digital

Digital (73, 174, 84)-net over F₃, using

t-expansion [i] based on digital (71, 174, 84)-net over F₃, using
- net from sequence [i] based on digital (71, 83)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(174−101, 174, 388)-Net in Base 3 — Upper bound on s

There is no (73, 174, 389)-net in base 3, because

1 times m-reduction [i] would yield (73, 173, 389)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 36092 642774 101007 539466 872162 337859 610250 631141 602740 618760 800159 500272 027415 327249 > 3¹⁷³ [i]