MinT - Best Known (212−59, 212, s)-Nets in Base 3

Best Known (212−59, 212, s)-Nets in Base 3

(212−59, 212, 288)-Net over F₃ — Constructive and digital

Digital (153, 212, 288)-net over F₃, using

1 times m-reduction [i] based on digital (153, 213, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 71, 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]

(212−59, 212, 599)-Net over F₃ — Digital

Digital (153, 212, 599)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−59, 212, 17252)-Net in Base 3 — Upper bound on s

There is no (153, 212, 17253)-net in base 3, because

1 times m-reduction [i] would yield (153, 211, 17253)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47117 081835 319189 341340 282577 528713 484173 674300 324238 817353 682906 807608 509361 335252 498946 365661 779067 > 3²¹¹ [i]