MinT - Best Known (225−63, 225, s)-Nets in Base 3

Best Known (225−63, 225, s)-Nets in Base 3

(225−63, 225, 288)-Net over F₃ — Constructive and digital

Digital (162, 225, 288)-net over F₃, using

t-expansion [i] based on digital (161, 225, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 75, 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]

(225−63, 225, 617)-Net over F₃ — Digital

Digital (162, 225, 617)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−63, 225, 17371)-Net in Base 3 — Upper bound on s

There is no (162, 225, 17372)-net in base 3, because

1 times m-reduction [i] would yield (162, 224, 17372)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75136 636070 306461 353163 304538 914379 690013 328354 754429 301119 198705 001226 963703 074267 220599 454010 867636 485585 > 3²²⁴ [i]