MinT - Best Known (11, 11+27, s)-Nets in Base 27

Best Known (11, 11+27, s)-Nets in Base 27

(11, 11+27, 96)-Net over F₂₇ — Constructive and digital

Digital (11, 38, 96)-net over F₂₇, using

net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
  - an explicitly constructive algebraic function field [i]

(11, 11+27, 100)-Net in Base 27 — Constructive

(11, 38, 100)-net in base 27, using

2 times m-reduction [i] based on (11, 40, 100)-net in base 27, using
- base change [i] based on digital (1, 30, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(11, 11+27, 100)-Net over F₂₇ — Digital

Digital (11, 38, 100)-net over F₂₇, using

net from sequence [i] based on digital (11, 99)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 100, using
  - a curve from the manYPoints database [i]

(11, 11+27, 2577)-Net in Base 27 — Upper bound on s

There is no (11, 38, 2578)-net in base 27, because

1 times m-reduction [i] would yield (11, 37, 2578)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 91465 989272 007172 166938 591296 815947 692301 882162 555677 > 27³⁷ [i]