MinT - Best Known (45−28, 45, s)-Nets in Base 27

Best Known (45−28, 45, s)-Nets in Base 27

(45−28, 45, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 45, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 45, 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]

(45−28, 45, 144)-Net over F₂₇ — Digital

Digital (17, 45, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 45, 144)-net over F₂₇, using
- net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
    - a curve from the manYPoints database [i]

(45−28, 45, 160)-Net in Base 27 — Constructive

(17, 45, 160)-net in base 27, using

3 times m-reduction [i] based on (17, 48, 160)-net in base 27, using
- base change [i] based on digital (5, 36, 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]

(45−28, 45, 167)-Net in Base 27

(17, 45, 167)-net in base 27, using

3 times m-reduction [i] based on (17, 48, 167)-net in base 27, using
- base change [i] based on digital (5, 36, 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]

(45−28, 45, 9267)-Net in Base 27 — Upper bound on s

There is no (17, 45, 9268)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 25801 072404 571052 005861 103295 174215 990046 445552 965409 333946 675961 > 27⁴⁵ [i]