MinT - Best Known (231−65, 231, s)-Nets in Base 3

Best Known (231−65, 231, s)-Nets in Base 3

(231−65, 231, 288)-Net over F₃ — Constructive and digital

Digital (166, 231, 288)-net over F₃, using

t-expansion [i] based on digital (165, 231, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 77, 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]

(231−65, 231, 621)-Net over F₃ — Digital

Digital (166, 231, 621)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−65, 231, 17153)-Net in Base 3 — Upper bound on s

There is no (166, 231, 17154)-net in base 3, because

1 times m-reduction [i] would yield (166, 230, 17154)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 696323 163611 583267 339019 538997 400893 905217 761559 069265 422759 445735 898113 844252 245106 108616 774543 886396 524865 > 3²³⁰ [i]