MinT - Best Known (25, 86, s)-Nets in Base 27

Best Known (25, 86, s)-Nets in Base 27

(25, 86, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 86, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 86, 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]

(25, 86, 116)-Net in Base 27 — Constructive

(25, 86, 116)-net in base 27, using

6 times m-reduction [i] based on (25, 92, 116)-net in base 27, using
- base change [i] based on digital (2, 69, 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]

(25, 86, 208)-Net over F₂₇ — Digital

Digital (25, 86, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 86, 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]

(25, 86, 5248)-Net in Base 27 — Upper bound on s

There is no (25, 86, 5249)-net in base 27, because

1 times m-reduction [i] would yield (25, 85, 5249)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 46 409751 733272 669777 158280 647928 294868 510815 455258 633664 813444 917123 318317 587444 999199 763413 461576 446768 709092 512153 762281 > 27⁸⁵ [i]