MinT - Best Known (238−63, 238, s)-Nets in Base 3

Best Known (238−63, 238, s)-Nets in Base 3

(238−63, 238, 288)-Net over F₃ — Constructive and digital

Digital (175, 238, 288)-net over F₃, using

8 times m-reduction [i] based on digital (175, 246, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 82, 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]

(238−63, 238, 791)-Net over F₃ — Digital

Digital (175, 238, 791)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−63, 238, 27554)-Net in Base 3 — Upper bound on s

There is no (175, 238, 27555)-net in base 3, because

1 times m-reduction [i] would yield (175, 237, 27555)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119676 226776 242872 150329 874634 153738 107778 341583 714191 659882 007301 371431 170025 003938 747918 505960 082297 261629 449811 > 3²³⁷ [i]