MinT - Best Known (144, 144+51, s)-Nets in Base 3

Best Known (144, 144+51, s)-Nets in Base 3

(144, 144+51, 288)-Net over F₃ — Constructive and digital

Digital (144, 195, 288)-net over F₃, using

t-expansion [i] based on digital (143, 195, 288)-net over F₃, using
- 3 times m-reduction [i] based on digital (143, 198, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 66, 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]

(144, 144+51, 699)-Net over F₃ — Digital

Digital (144, 195, 699)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+51, 25623)-Net in Base 3 — Upper bound on s

There is no (144, 195, 25624)-net in base 3, because

1 times m-reduction [i] would yield (144, 194, 25624)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 459568 408026 749409 239992 839478 267901 989991 334486 088311 728242 093109 334797 123942 627520 814001 > 3¹⁹⁴ [i]