MinT - Best Known (11, 11+25, s)-Nets in Base 27

Best Known (11, 11+25, s)-Nets in Base 27

(11, 11+25, 96)-Net over F₂₇ — Constructive and digital

Digital (11, 36, 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+25, 100)-Net over F₂₇ — Digital

Digital (11, 36, 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+25, 116)-Net in Base 27 — Constructive

(11, 36, 116)-net in base 27, using

base change [i] based on digital (2, 27, 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]

(11, 11+25, 118)-Net in Base 27

(11, 36, 118)-net in base 27, using

base change [i] based on digital (2, 27, 118)-net over F₈₁, using
- net from sequence [i] based on digital (2, 117)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 118, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(11, 11+25, 3036)-Net in Base 27 — Upper bound on s

There is no (11, 36, 3037)-net in base 27, because

1 times m-reduction [i] would yield (11, 35, 3037)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 125 572902 779591 842246 627416 023688 820285 223120 833489 > 27³⁵ [i]