MinT - Best Known (141−36, 141, s)-Nets in Base 3

Best Known (141−36, 141, s)-Nets in Base 3

(141−36, 141, 288)-Net over F₃ — Constructive and digital

Digital (105, 141, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 47, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(141−36, 141, 595)-Net over F₃ — Digital

Digital (105, 141, 595)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−36, 141, 20614)-Net in Base 3 — Upper bound on s

There is no (105, 141, 20615)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 798790 868750 656015 192155 762506 007150 405409 535722 700845 159097 906541 > 3¹⁴¹ [i]