MinT - Best Known (204−57, 204, s)-Nets in Base 3

Best Known (204−57, 204, s)-Nets in Base 3

(204−57, 204, 288)-Net over F₃ — Constructive and digital

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]

(204−57, 204, 571)-Net over F₃ — Digital

Digital (147, 204, 571)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−57, 204, 16231)-Net in Base 3 — Upper bound on s

There is no (147, 204, 16232)-net in base 3, because

1 times m-reduction [i] would yield (147, 203, 16232)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 172750 882510 616815 562938 359642 766597 235246 038928 968073 908889 458089 895230 208692 486651 115106 615361 > 3²⁰³ [i]