MinT - Best Known (10, 29, s)-Nets in Base 27

Best Known (10, 29, s)-Nets in Base 27

(10, 29, 94)-Net over F₂₇ — Constructive and digital

Digital (10, 29, 94)-net over F₂₇, using

net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
  - a function field by SÃ©mirat [i]

(10, 29, 99)-Net over F₂₇ — Digital

Digital (10, 29, 99)-net over F₂₇, using

t-expansion [i] based on digital (9, 29, 99)-net over F₂₇, using
- net from sequence [i] based on digital (9, 98)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 99, using
    - a curve from the manYPoints database [i]

(10, 29, 116)-Net in Base 27 — Constructive

(10, 29, 116)-net in base 27, using

3 times m-reduction [i] based on (10, 32, 116)-net in base 27, using
- base change [i] based on digital (2, 24, 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]

(10, 29, 118)-Net in Base 27

(10, 29, 118)-net in base 27, using

3 times m-reduction [i] based on (10, 32, 118)-net in base 27, using
- base change [i] based on digital (2, 24, 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]

(10, 29, 4523)-Net in Base 27 — Upper bound on s

There is no (10, 29, 4524)-net in base 27, because

1 times m-reduction [i] would yield (10, 28, 4524)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 11979 887726 640849 991178 599274 979417 264377 > 27²⁸ [i]