MinT - Best Known (213−58, 213, s)-Nets in Base 3

Best Known (213−58, 213, s)-Nets in Base 3

(213−58, 213, 288)-Net over F₃ — Constructive and digital

Digital (155, 213, 288)-net over F₃, using

3 times m-reduction [i] based on digital (155, 216, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 72, 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]

(213−58, 213, 649)-Net over F₃ — Digital

Digital (155, 213, 649)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−58, 213, 18612)-Net in Base 3 — Upper bound on s

There is no (155, 213, 18613)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423900 141106 972875 474183 628374 741562 100684 304707 992702 715095 700744 808050 516269 062808 647485 318525 375259 > 3²¹³ [i]