MinT - Best Known (146, 146+55, s)-Nets in Base 3

Best Known (146, 146+55, s)-Nets in Base 3

(146, 146+55, 288)-Net over F₃ — Constructive and digital

Digital (146, 201, 288)-net over F₃, using

t-expansion [i] based on digital (145, 201, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 67, 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]

(146, 146+55, 607)-Net over F₃ — Digital

Digital (146, 201, 607)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+55, 18663)-Net in Base 3 — Upper bound on s

There is no (146, 201, 18664)-net in base 3, because

1 times m-reduction [i] would yield (146, 200, 18664)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265816 584940 309751 183393 105706 234548 282196 071119 067969 325287 746636 880661 947546 869921 791313 463585 > 3²⁰⁰ [i]