MinT - Best Known (222−59, 222, s)-Nets in Base 3

Best Known (222−59, 222, s)-Nets in Base 3

(222−59, 222, 288)-Net over F₃ — Constructive and digital

Digital (163, 222, 288)-net over F₃, using

6 times m-reduction [i] based on digital (163, 228, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 76, 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]

(222−59, 222, 734)-Net over F₃ — Digital

Digital (163, 222, 734)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−59, 222, 25211)-Net in Base 3 — Upper bound on s

There is no (163, 222, 25212)-net in base 3, because

1 times m-reduction [i] would yield (163, 221, 25212)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2780 769596 811573 051063 720731 522261 685820 380207 017345 233315 396805 038531 504139 402311 878658 893800 917740 252633 > 3²²¹ [i]