MinT - Best Known (173−79, 173, s)-Nets in Base 3

Best Known (173−79, 173, s)-Nets in Base 3

(173−79, 173, 74)-Net over F₃ — Constructive and digital

Digital (94, 173, 74)-net over F₃, using

1 times m-reduction [i] based on digital (94, 174, 74)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 67, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
  2. digital (27, 107, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(173−79, 173, 114)-Net over F₃ — Digital

Digital (94, 173, 114)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−79, 173, 940)-Net in Base 3 — Upper bound on s

There is no (94, 173, 941)-net in base 3, because

1 times m-reduction [i] would yield (94, 172, 941)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11723 482798 802609 466530 923597 891661 584652 959839 377549 446285 687399 522905 175864 353019 > 3¹⁷² [i]