MinT - Best Known (203−55, 203, s)-Nets in Base 3

Best Known (203−55, 203, s)-Nets in Base 3

(203−55, 203, 288)-Net over F₃ — Constructive and digital

Digital (148, 203, 288)-net over F₃, using

t-expansion [i] based on digital (147, 203, 288)-net over F₃, using
- 1 times m-reduction [i] based on digital (147, 204, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 68, 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]

(203−55, 203, 635)-Net over F₃ — Digital

Digital (148, 203, 635)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−55, 203, 20248)-Net in Base 3 — Upper bound on s

There is no (148, 203, 20249)-net in base 3, because

1 times m-reduction [i] would yield (148, 202, 20249)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 393597 876988 425894 184725 369009 326177 217099 616437 255716 010383 173526 618040 275930 109718 893186 964187 > 3²⁰² [i]