MinT - Best Known (24, 110, s)-Nets in Base 27

Best Known (24, 110, s)-Nets in Base 27

(24, 110, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 110, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 110, 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]

(24, 110, 208)-Net over F₂₇ — Digital

Digital (24, 110, 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]

(24, 110, 2956)-Net in Base 27 — Upper bound on s

There is no (24, 110, 2957)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 28 287843 107161 885230 667428 243216 376637 798445 775962 377776 272330 401490 758646 617594 537298 175357 805312 913784 502533 018492 849712 825769 788158 643147 235726 065432 075475 > 27¹¹⁰ [i]