MinT - Best Known (32, 103, s)-Nets in Base 27

Best Known (32, 103, s)-Nets in Base 27

(32, 103, 114)-Net over F₂₇ — Constructive and digital

Digital (32, 103, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 103, 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]

(32, 103, 160)-Net in Base 27 — Constructive

(32, 103, 160)-net in base 27, using

5 times m-reduction [i] based on (32, 108, 160)-net in base 27, using
- base change [i] based on digital (5, 81, 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]

(32, 103, 208)-Net over F₂₇ — Digital

Digital (32, 103, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 103, 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]

(32, 103, 7919)-Net in Base 27 — Upper bound on s

There is no (32, 103, 7920)-net in base 27, because

1 times m-reduction [i] would yield (32, 102, 7920)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 100 084688 861031 251108 882930 271626 116787 380825 770162 333671 930999 215042 841458 761326 497868 468499 555551 536630 166862 156855 113094 544507 953908 927016 269377 > 27¹⁰² [i]