MinT - Best Known (26, 26+52, s)-Nets in Base 27

Best Known (26, 26+52, s)-Nets in Base 27

(26, 26+52, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 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]

(26, 26+52, 160)-Net in Base 27 — Constructive

(26, 78, 160)-net in base 27, using

6 times m-reduction [i] based on (26, 84, 160)-net in base 27, using
- base change [i] based on digital (5, 63, 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]

(26, 26+52, 208)-Net over F₂₇ — Digital

Digital (26, 78, 208)-net over F₂₇, using

t-expansion [i] based on 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]

(26, 26+52, 7974)-Net in Base 27 — Upper bound on s

There is no (26, 78, 7975)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 4444 029952 413247 289085 225094 858541 340154 847981 061232 801883 468437 830809 081208 509754 358446 604453 909298 860274 073645 > 27⁷⁸ [i]