MinT - Best Known (24, 78, s)-Nets in Base 27

Best Known (24, 78, s)-Nets in Base 27

(24, 78, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 78, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 78, 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, 78, 150)-Net in Base 27 — Constructive

(24, 78, 150)-net in base 27, using

2 times m-reduction [i] based on (24, 80, 150)-net in base 27, using
- base change [i] based on digital (4, 60, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(24, 78, 208)-Net over F₂₇ — Digital

Digital (24, 78, 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, 78, 5720)-Net in Base 27 — Upper bound on s

There is no (24, 78, 5721)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 4443 885285 143820 820457 618386 609902 906687 896938 353717 698812 949548 548668 343485 568422 401143 771598 220115 330939 192995 > 27⁷⁸ [i]