MinT - Best Known (101−71, 101, s)-Nets in Base 27

Best Known (101−71, 101, s)-Nets in Base 27

(101−71, 101, 114)-Net over F₂₇ — Constructive and digital

Digital (30, 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]

(101−71, 101, 150)-Net in Base 27 — Constructive

(30, 101, 150)-net in base 27, using

3 times m-reduction [i] based on (30, 104, 150)-net in base 27, using
- base change [i] based on digital (4, 78, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(101−71, 101, 208)-Net over F₂₇ — Digital

Digital (30, 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]

(101−71, 101, 6556)-Net in Base 27 — Upper bound on s

There is no (30, 101, 6557)-net in base 27, because

1 times m-reduction [i] would yield (30, 100, 6557)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 137075 547771 660800 104561 332060 344653 432718 042138 050741 459533 032573 335496 695148 772702 053517 784170 930519 172198 876045 421233 968709 899892 750056 554547 > 27¹⁰⁰ [i]