MinT - Best Known (29, 29+54, s)-Nets in Base 27

Best Known (29, 29+54, s)-Nets in Base 27

(29, 29+54, 114)-Net over F₂₇ — Constructive and digital

Digital (29, 83, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 83, 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]

(29, 29+54, 172)-Net in Base 27 — Constructive

(29, 83, 172)-net in base 27, using

5 times m-reduction [i] based on (29, 88, 172)-net in base 27, using
- base change [i] based on digital (7, 66, 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]

(29, 29+54, 208)-Net over F₂₇ — Digital

Digital (29, 83, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 83, 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]

(29, 29+54, 226)-Net in Base 27

(29, 83, 226)-net in base 27, using

1 times m-reduction [i] based on (29, 84, 226)-net in base 27, using
- base change [i] based on digital (8, 63, 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]

(29, 29+54, 10543)-Net in Base 27 — Upper bound on s

There is no (29, 83, 10544)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 63685 478040 996891 765927 024642 548614 449227 036067 385443 864400 259868 032566 016594 659741 612152 164946 212904 888926 365564 847937 > 27⁸³ [i]