MinT - Best Known (240−63, 240, s)-Nets in Base 3

Best Known (240−63, 240, s)-Nets in Base 3

(240−63, 240, 288)-Net over F₃ — Constructive and digital

Digital (177, 240, 288)-net over F₃, using

9 times m-reduction [i] based on digital (177, 249, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 83, 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]

(240−63, 240, 821)-Net over F₃ — Digital

Digital (177, 240, 821)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−63, 240, 29580)-Net in Base 3 — Upper bound on s

There is no (177, 240, 29581)-net in base 3, because

1 times m-reduction [i] would yield (177, 239, 29581)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 076898 484856 452209 699872 826908 651362 569698 187037 196039 227009 081646 398725 775143 865670 114205 689675 232235 379216 442075 > 3²³⁹ [i]