MinT - Best Known (31, 89, s)-Nets in Base 27

Best Known (31, 89, s)-Nets in Base 27

(31, 89, 114)-Net over F₂₇ — Constructive and digital

Digital (31, 89, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 89, 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]

(31, 89, 172)-Net in Base 27 — Constructive

(31, 89, 172)-net in base 27, using

7 times m-reduction [i] based on (31, 96, 172)-net in base 27, using
- base change [i] based on digital (7, 72, 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]

(31, 89, 208)-Net over F₂₇ — Digital

Digital (31, 89, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 89, 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]

(31, 89, 226)-Net in Base 27

(31, 89, 226)-net in base 27, using

3 times m-reduction [i] based on (31, 92, 226)-net in base 27, using
- base change [i] based on digital (8, 69, 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]

(31, 89, 11075)-Net in Base 27 — Upper bound on s

There is no (31, 89, 11076)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 24 658378 131554 070554 474257 289587 785366 000045 588261 364474 384556 354359 722533 916211 393439 029318 460618 125785 033441 476352 540815 780425 > 27⁸⁹ [i]