MinT - Best Known (27, 27+66, s)-Nets in Base 27

Best Known (27, 27+66, s)-Nets in Base 27

(27, 27+66, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 93, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 93, 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]

(27, 27+66, 116)-Net in Base 27 — Constructive

(27, 93, 116)-net in base 27, using

7 times m-reduction [i] based on (27, 100, 116)-net in base 27, using
- base change [i] based on digital (2, 75, 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]

(27, 27+66, 208)-Net over F₂₇ — Digital

Digital (27, 93, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 93, 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]

(27, 27+66, 5455)-Net in Base 27 — Upper bound on s

There is no (27, 93, 5456)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 13 108343 822002 372123 619931 435654 765628 953466 845044 278906 814796 270585 267683 953478 129101 712810 938331 840091 926591 038927 608728 089264 031265 > 27⁹³ [i]