MinT - Best Known (236−65, 236, s)-Nets in Base 3

Best Known (236−65, 236, s)-Nets in Base 3

(236−65, 236, 288)-Net over F₃ — Constructive and digital

Digital (171, 236, 288)-net over F₃, using

4 times m-reduction [i] based on digital (171, 240, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 80, 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]

(236−65, 236, 681)-Net over F₃ — Digital

Digital (171, 236, 681)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−65, 236, 20372)-Net in Base 3 — Upper bound on s

There is no (171, 236, 20373)-net in base 3, because

1 times m-reduction [i] would yield (171, 235, 20373)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13304 694717 527703 792348 970361 102884 585930 878237 353117 199667 055864 365677 870495 312962 763271 229757 337326 270936 479617 > 3²³⁵ [i]