MinT - Best Known (33, 62, s)-Nets in Base 5

Best Known (33, 62, s)-Nets in Base 5

(33, 62, 72)-Net over F₅ — Constructive and digital

Digital (33, 62, 72)-net over F₅, using

t-expansion [i] based on digital (31, 62, 72)-net over F₅, using
- net from sequence [i] based on digital (31, 71)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
    - an explicitly constructive algebraic function field [i]

(33, 62, 92)-Net over F₅ — Digital

Digital (33, 62, 92)-net over F₅, using

trace code for nets [i] based on digital (2, 31, 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]

(33, 62, 1668)-Net in Base 5 — Upper bound on s

There is no (33, 62, 1669)-net in base 5, because

1 times m-reduction [i] would yield (33, 61, 1669)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 355746 845888 300537 326454 566558 835263 090025 > 5⁶¹ [i]