MinT - Best Known (31−18, 31, s)-Nets in Base 27

Best Known (31−18, 31, s)-Nets in Base 27

(31−18, 31, 96)-Net over F₂₇ — Constructive and digital

Digital (13, 31, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 31, 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]

(31−18, 31, 136)-Net over F₂₇ — Digital

Digital (13, 31, 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]

(31−18, 31, 160)-Net in Base 27 — Constructive

(13, 31, 160)-net in base 27, using

1 times m-reduction [i] based on (13, 32, 160)-net in base 27, using
- base change [i] based on digital (5, 24, 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]

(31−18, 31, 167)-Net in Base 27

(13, 31, 167)-net in base 27, using

1 times m-reduction [i] based on (13, 32, 167)-net in base 27, using
- base change [i] based on digital (5, 24, 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]

(31−18, 31, 13579)-Net in Base 27 — Upper bound on s

There is no (13, 31, 13580)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 235 692441 218748 279266 488943 064546 308180 859577 > 27³¹ [i]