MinT - Best Known (169−96, 169, s)-Nets in Base 3

Best Known (169−96, 169, s)-Nets in Base 3

(169−96, 169, 48)-Net over F₃ — Constructive and digital

Digital (73, 169, 48)-net over F₃, using

t-expansion [i] based on digital (45, 169, 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]

(169−96, 169, 84)-Net over F₃ — Digital

Digital (73, 169, 84)-net over F₃, using

t-expansion [i] based on digital (71, 169, 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]

(169−96, 169, 402)-Net in Base 3 — Upper bound on s

There is no (73, 169, 403)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 437 428828 068082 722424 512850 745934 404198 437780 627506 642362 130861 632706 393930 205345 > 3¹⁶⁹ [i]