MinT - Best Known (26, 26+56, s)-Nets in Base 27

Best Known (26, 26+56, s)-Nets in Base 27

(26, 26+56, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 82, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 82, 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+56, 160)-Net in Base 27 — Constructive

(26, 82, 160)-net in base 27, using

2 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+56, 208)-Net over F₂₇ — Digital

Digital (26, 82, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 82, 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+56, 6744)-Net in Base 27 — Upper bound on s

There is no (26, 82, 6745)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2359 644811 121851 541210 087286 188550 786031 710829 322576 605342 841037 989039 655233 649464 407185 503279 615919 818317 944966 426321 > 27⁸² [i]