MinT - Best Known (149, 149+53, s)-Nets in Base 3

Best Known (149, 149+53, s)-Nets in Base 3

(149, 149+53, 288)-Net over F₃ — Constructive and digital

Digital (149, 202, 288)-net over F₃, using

5 times m-reduction [i] based on digital (149, 207, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 69, 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]

(149, 149+53, 711)-Net over F₃ — Digital

Digital (149, 202, 711)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+53, 25724)-Net in Base 3 — Upper bound on s

There is no (149, 202, 25725)-net in base 3, because

1 times m-reduction [i] would yield (149, 201, 25725)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 797229 855865 470407 596823 079835 913429 963132 960357 471843 653860 239620 940779 350998 331690 315529 452129 > 3²⁰¹ [i]