MinT - Best Known (230−61, 230, s)-Nets in Base 3

Best Known (230−61, 230, s)-Nets in Base 3

(230−61, 230, 288)-Net over F₃ — Constructive and digital

Digital (169, 230, 288)-net over F₃, using

7 times m-reduction [i] based on digital (169, 237, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 79, 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]

(230−61, 230, 762)-Net over F₃ — Digital

Digital (169, 230, 762)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−61, 230, 26381)-Net in Base 3 — Upper bound on s

There is no (169, 230, 26382)-net in base 3, because

1 times m-reduction [i] would yield (169, 229, 26382)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 240007 631372 248983 972391 554355 092016 379643 131787 067213 128332 991464 502298 326452 903805 575416 941593 240418 109365 > 3²²⁹ [i]