MinT - Best Known (78, 78+74, s)-Nets in Base 3

Best Known (78, 78+74, s)-Nets in Base 3

(78, 78+74, 64)-Net over F₃ — Constructive and digital

Digital (78, 152, 64)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 52, 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, 100, 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]

(78, 78+74, 85)-Net over F₃ — Digital

Digital (78, 152, 85)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+74, 632)-Net in Base 3 — Upper bound on s

There is no (78, 152, 633)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 409984 891957 680419 295856 329034 106018 575848 972690 037362 661984 522346 863331 > 3¹⁵² [i]