MinT - Best Known (199−98, 199, s)-Nets in Base 3

Best Known (199−98, 199, s)-Nets in Base 3

(199−98, 199, 72)-Net over F₃ — Constructive and digital

Digital (101, 199, 72)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 75, 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 (26, 124, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃ (see above)

(199−98, 199, 104)-Net over F₃ — Digital

Digital (101, 199, 104)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−98, 199, 780)-Net in Base 3 — Upper bound on s

There is no (101, 199, 781)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 90972 816510 808200 763861 438053 147998 731542 223597 590006 820863 018807 322039 421374 331361 398831 880795 > 3¹⁹⁹ [i]