MinT - Best Known (204−56, 204, s)-Nets in Base 3

Best Known (204−56, 204, s)-Nets in Base 3

(204−56, 204, 288)-Net over F₃ — Constructive and digital

Digital (148, 204, 288)-net over F₃, using

t-expansion [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]

(204−56, 204, 608)-Net over F₃ — Digital

Digital (148, 204, 608)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−56, 204, 16882)-Net in Base 3 — Upper bound on s

There is no (148, 204, 16883)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 531098 665031 623356 084062 823193 191267 795307 933083 192564 926706 085616 964103 352721 617029 350478 015273 > 3²⁰⁴ [i]