MinT - Best Known (91−63, 91, s)-Nets in Base 27

Best Known (91−63, 91, s)-Nets in Base 27

(91−63, 91, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 91, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 91, 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]

(91−63, 91, 160)-Net in Base 27 — Constructive

(28, 91, 160)-net in base 27, using

1 times m-reduction [i] based on (28, 92, 160)-net in base 27, using
- base change [i] based on digital (5, 69, 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]

(91−63, 91, 208)-Net over F₂₇ — Digital

Digital (28, 91, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 91, 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]

(91−63, 91, 6817)-Net in Base 27 — Upper bound on s

There is no (28, 91, 6818)-net in base 27, because

1 times m-reduction [i] would yield (28, 90, 6818)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 667 479906 123264 739711 348567 602604 732605 625745 295404 769579 335042 490707 662856 495527 265801 946912 761520 006124 289167 185501 204073 419945 > 27⁹⁰ [i]