MinT - Best Known (77−52, 77, s)-Nets in Base 27

Best Known (77−52, 77, s)-Nets in Base 27

(77−52, 77, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 77, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 77, 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]

(77−52, 77, 160)-Net in Base 27 — Constructive

(25, 77, 160)-net in base 27, using

3 times m-reduction [i] based on (25, 80, 160)-net in base 27, using
- base change [i] based on digital (5, 60, 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]

(77−52, 77, 208)-Net over F₂₇ — Digital

Digital (25, 77, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 77, 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]

(77−52, 77, 7023)-Net in Base 27 — Upper bound on s

There is no (25, 77, 7024)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 164 648302 125995 868880 405239 506772 936538 733745 332532 888406 628732 946224 461482 648526 336978 843753 808073 063651 307425 > 27⁷⁷ [i]