MinT - Best Known (35−15, 35, s)-Nets in Base 5

Best Known (35−15, 35, s)-Nets in Base 5

(35−15, 35, 56)-Net over F₅ — Constructive and digital

Digital (20, 35, 56)-net over F₅, using

1 times m-reduction [i] based on digital (20, 36, 56)-net over F₅, using
- trace code for nets [i] based on digital (2, 18, 28)-net over F₂₅, using
  - net from sequence [i] based on digital (2, 27)-sequence over F₂₅, using
    - Niederreiter sequence [i]

(35−15, 35, 92)-Net over F₅ — Digital

Digital (20, 35, 92)-net over F₅, using

1 times m-reduction [i] based on digital (20, 36, 92)-net over F₅, using
- trace code for nets [i] based on digital (2, 18, 46)-net over F₂₅, using
  - net from sequence [i] based on digital (2, 45)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 2 and N(F) ≥ 46, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(35−15, 35, 2093)-Net in Base 5 — Upper bound on s

There is no (20, 35, 2094)-net in base 5, because

1 times m-reduction [i] would yield (20, 34, 2094)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 583053 575025 042811 135961 > 5³⁴ [i]