MinT - Best Known (14, 14+30, s)-Nets in Base 27

Best Known (14, 14+30, s)-Nets in Base 27

(14, 14+30, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 44, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 44, 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+30, 116)-Net in Base 27 — Constructive

(14, 44, 116)-net in base 27, using

4 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]

(14, 14+30, 136)-Net over F₂₇ — Digital

Digital (14, 44, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 44, 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+30, 3895)-Net in Base 27 — Upper bound on s

There is no (14, 44, 3896)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 955 071654 956862 781083 143736 435242 459115 924843 859638 137097 006561 > 27⁴⁴ [i]