MinT - Best Known (198−51, 198, s)-Nets in Base 3

Best Known (198−51, 198, s)-Nets in Base 3

(198−51, 198, 288)-Net over F₃ — Constructive and digital

Digital (147, 198, 288)-net over F₃, using

6 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]

(198−51, 198, 750)-Net over F₃ — Digital

Digital (147, 198, 750)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−51, 198, 29238)-Net in Base 3 — Upper bound on s

There is no (147, 198, 29239)-net in base 3, because

1 times m-reduction [i] would yield (147, 197, 29239)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9845 952278 687516 070182 344823 655437 028133 444616 521075 275226 165385 346621 196050 406823 026644 584511 > 3¹⁹⁷ [i]