MinT - Best Known (182−86, 182, s)-Nets in Base 3

Best Known (182−86, 182, s)-Nets in Base 3

(182−86, 182, 73)-Net over F₃ — Constructive and digital

Digital (96, 182, 73)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 69, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [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, 113, 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]

(182−86, 182, 108)-Net over F₃ — Digital

Digital (96, 182, 108)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−86, 182, 841)-Net in Base 3 — Upper bound on s

There is no (96, 182, 842)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 713 836616 847556 388926 099598 966895 752638 019687 702931 074169 673007 521951 655557 783780 219425 > 3¹⁸² [i]