MinT - Best Known (24, 24+63, s)-Nets in Base 27

Best Known (24, 24+63, s)-Nets in Base 27

(24, 24+63, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 87, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 87, 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, 24+63, 116)-Net in Base 27 — Constructive

(24, 87, 116)-net in base 27, using

1 times m-reduction [i] based on (24, 88, 116)-net in base 27, using
- base change [i] based on digital (2, 66, 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]

(24, 24+63, 208)-Net over F₂₇ — Digital

Digital (24, 87, 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, 24+63, 4450)-Net in Base 27 — Upper bound on s

There is no (24, 87, 4451)-net in base 27, because

1 times m-reduction [i] would yield (24, 86, 4451)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1259 466566 843119 408390 469026 652599 075095 244556 344375 273968 702657 606575 354869 731012 905149 440592 467183 448732 573199 239023 632395 > 27⁸⁶ [i]