MinT - Best Known (247−69, 247, s)-Nets in Base 3

Best Known (247−69, 247, s)-Nets in Base 3

(247−69, 247, 288)-Net over F₃ — Constructive and digital

Digital (178, 247, 288)-net over F₃, using

t-expansion [i] based on digital (177, 247, 288)-net over F₃, using
- 2 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]

(247−69, 247, 675)-Net over F₃ — Digital

Digital (178, 247, 675)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−69, 247, 19133)-Net in Base 3 — Upper bound on s

There is no (178, 247, 19134)-net in base 3, because

1 times m-reduction [i] would yield (178, 246, 19134)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2355 388054 566662 992724 699540 241467 985324 849322 679521 832694 649964 251123 043011 235106 142799 675091 119924 029657 031059 002045 > 3²⁴⁶ [i]