MinT - Best Known (239−64, 239, s)-Nets in Base 3

Best Known (239−64, 239, s)-Nets in Base 3

(239−64, 239, 288)-Net over F₃ — Constructive and digital

Digital (175, 239, 288)-net over F₃, using

7 times m-reduction [i] based on digital (175, 246, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 82, 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]

(239−64, 239, 761)-Net over F₃ — Digital

Digital (175, 239, 761)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−64, 239, 23375)-Net in Base 3 — Upper bound on s

There is no (175, 239, 23376)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 076808 887398 573047 175387 539364 469043 002840 038862 159106 908400 253537 114293 423453 566278 476005 370012 809848 082398 484481 > 3²³⁹ [i]