MinT - Best Known (241−67, 241, s)-Nets in Base 3

Best Known (241−67, 241, s)-Nets in Base 3

(241−67, 241, 288)-Net over F₃ — Constructive and digital

Digital (174, 241, 288)-net over F₃, using

t-expansion [i] based on digital (173, 241, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (173, 243, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 81, 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]

(241−67, 241, 671)-Net over F₃ — Digital

Digital (174, 241, 671)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−67, 241, 19389)-Net in Base 3 — Upper bound on s

There is no (174, 241, 19390)-net in base 3, because

1 times m-reduction [i] would yield (174, 240, 19390)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 231146 972776 908541 579793 592546 658769 885641 819470 030977 669639 072389 677069 246125 917272 498748 537122 389823 058218 172221 > 3²⁴⁰ [i]