MinT - Best Known (31, 31+70, s)-Nets in Base 27

Best Known (31, 31+70, s)-Nets in Base 27

(31, 31+70, 114)-Net over F₂₇ — Constructive and digital

Digital (31, 101, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 101, 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]

(31, 31+70, 160)-Net in Base 27 — Constructive

(31, 101, 160)-net in base 27, using

3 times m-reduction [i] based on (31, 104, 160)-net in base 27, using
- base change [i] based on digital (5, 78, 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]

(31, 31+70, 208)-Net over F₂₇ — Digital

Digital (31, 101, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 101, 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]

(31, 31+70, 7205)-Net in Base 27 — Upper bound on s

There is no (31, 101, 7206)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 3 696254 885535 496901 803096 597698 184335 177940 205715 654276 236008 679521 140232 508696 006282 457682 612867 706568 245235 467330 499918 629457 703928 465848 134705 > 27¹⁰¹ [i]