MinT - Best Known (14, 14+36, s)-Nets in Base 27

Best Known (14, 14+36, s)-Nets in Base 27

(14, 14+36, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 50, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 50, 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]

(14, 14+36, 100)-Net in Base 27 — Constructive

(14, 50, 100)-net in base 27, using

2 times m-reduction [i] based on (14, 52, 100)-net in base 27, using
- base change [i] based on digital (1, 39, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(14, 14+36, 136)-Net over F₂₇ — Digital

Digital (14, 50, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 50, 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]

(14, 14+36, 2739)-Net in Base 27 — Upper bound on s

There is no (14, 50, 2740)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 370553 719631 968068 294557 923748 966360 009672 882609 132904 993530 094327 153753 > 27⁵⁰ [i]