MinT - Best Known (73, 171, s)-Nets in Base 3

Best Known (73, 171, s)-Nets in Base 3

(73, 171, 48)-Net over F₃ — Constructive and digital

Digital (73, 171, 48)-net over F₃, using

t-expansion [i] based on digital (45, 171, 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]

(73, 171, 84)-Net over F₃ — Digital

Digital (73, 171, 84)-net over F₃, using

t-expansion [i] based on digital (71, 171, 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]

(73, 171, 395)-Net in Base 3 — Upper bound on s

There is no (73, 171, 396)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4089 655010 498432 748320 173408 524698 595001 980769 686269 478865 806037 749233 582502 633753 > 3¹⁷¹ [i]