MinT - Best Known (165−92, 165, s)-Nets in Base 3

Best Known (165−92, 165, s)-Nets in Base 3

(165−92, 165, 48)-Net over F₃ — Constructive and digital

Digital (73, 165, 48)-net over F₃, using

t-expansion [i] based on digital (45, 165, 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]

(165−92, 165, 84)-Net over F₃ — Digital

Digital (73, 165, 84)-net over F₃, using

t-expansion [i] based on digital (71, 165, 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]

(165−92, 165, 419)-Net in Base 3 — Upper bound on s

There is no (73, 165, 420)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5 690175 027749 935063 138705 192731 971084 935101 878862 536545 251762 694470 477874 083225 > 3¹⁶⁵ [i]