MinT - Best Known (37−22, 37, s)-Nets in Base 27

Best Known (37−22, 37, s)-Nets in Base 27

(37−22, 37, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 37, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 37, 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]

(37−22, 37, 136)-Net over F₂₇ — Digital

Digital (15, 37, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 37, 136)-net over F₂₇, using
- net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(37−22, 37, 160)-Net in Base 27 — Constructive

(15, 37, 160)-net in base 27, using

3 times m-reduction [i] based on (15, 40, 160)-net in base 27, using
- base change [i] based on digital (5, 30, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(37−22, 37, 167)-Net in Base 27

(15, 37, 167)-net in base 27, using

3 times m-reduction [i] based on (15, 40, 167)-net in base 27, using
- base change [i] based on digital (5, 30, 167)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
      - a curve from the manYPoints database [i]

(37−22, 37, 12315)-Net in Base 27 — Upper bound on s

There is no (15, 37, 12316)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 91373 540677 515577 505246 406183 690463 307292 515915 601393 > 27³⁷ [i]