MinT - Best Known (76, 76+70, s)-Nets in Base 3

Best Known (76, 76+70, s)-Nets in Base 3

(76, 76+70, 64)-Net over F₃ — Constructive and digital

Digital (76, 146, 64)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 50, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
2. digital (26, 96, 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]

(76, 76+70, 86)-Net over F₃ — Digital

Digital (76, 146, 86)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+70, 646)-Net in Base 3 — Upper bound on s

There is no (76, 146, 647)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4756 345123 309109 623353 508502 175861 820393 597459 833945 776998 550796 037083 > 3¹⁴⁶ [i]