MinT - Best Known (25, 92, s)-Nets in Base 27

Best Known (25, 92, s)-Nets in Base 27

(25, 92, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 92, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 92, 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, 92, 116)-Net in Base 27 — Constructive

(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, 92, 208)-Net over F₂₇ — Digital

Digital (25, 92, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 92, 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, 92, 4464)-Net in Base 27 — Upper bound on s

There is no (25, 92, 4465)-net in base 27, because

1 times m-reduction [i] would yield (25, 91, 4465)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 17981 231996 510239 991367 758060 850976 300829 657254 583652 683248 922134 093386 882640 820600 020715 520278 536441 807069 210882 397038 192828 129275 > 27⁹¹ [i]