MinT - Best Known (27, 27+49, s)-Nets in Base 27

Best Known (27, 27+49, s)-Nets in Base 27

(27, 27+49, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 76, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 76, 114)-net over F₂₇, using
- net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
    - an explicitly constructive algebraic function field [i]

(27, 27+49, 172)-Net in Base 27 — Constructive

(27, 76, 172)-net in base 27, using

4 times m-reduction [i] based on (27, 80, 172)-net in base 27, using
- base change [i] based on digital (7, 60, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(27, 27+49, 208)-Net over F₂₇ — Digital

Digital (27, 76, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 76, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(27, 27+49, 226)-Net in Base 27

(27, 76, 226)-net in base 27, using

base change [i] based on digital (8, 57, 226)-net over F₈₁, using
- net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
    - a curve from the manYPoints database [i]

(27, 27+49, 11192)-Net in Base 27 — Upper bound on s

There is no (27, 76, 11193)-net in base 27, because

1 times m-reduction [i] would yield (27, 75, 11193)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 225387 581880 964107 278880 178029 237907 865235 568327 897896 633567 284548 403060 558814 296017 335356 268693 874745 811873 > 27⁷⁵ [i]