MinT - Best Known (41−27, 41, s)-Nets in Base 27

Best Known (41−27, 41, s)-Nets in Base 27

(41−27, 41, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 41, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 41, 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]

(41−27, 41, 116)-Net in Base 27 — Constructive

(14, 41, 116)-net in base 27, using

7 times m-reduction [i] based on (14, 48, 116)-net in base 27, using
- base change [i] based on digital (2, 36, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(41−27, 41, 136)-Net over F₂₇ — Digital

Digital (14, 41, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 41, 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]

(41−27, 41, 5522)-Net in Base 27 — Upper bound on s

There is no (14, 41, 5523)-net in base 27, because

1 times m-reduction [i] would yield (14, 40, 5523)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1800 062360 980342 014304 504183 282214 777791 277329 469984 749303 > 27⁴⁰ [i]