MinT - Best Known (231−62, 231, s)-Nets in Base 3

Best Known (231−62, 231, s)-Nets in Base 3

(231−62, 231, 288)-Net over F₃ — Constructive and digital

Digital (169, 231, 288)-net over F₃, using

6 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]

(231−62, 231, 733)-Net over F₃ — Digital

Digital (169, 231, 733)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−62, 231, 22270)-Net in Base 3 — Upper bound on s

There is no (169, 231, 22271)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 154917 597784 546282 614195 582158 756458 302437 819776 205035 881808 753981 924883 825641 128219 110238 452665 641397 877699 > 3²³¹ [i]