MinT - Best Known (21−19, 21, s)-Nets in Base 25

Best Known (21−19, 21, s)-Nets in Base 25

(21−19, 21, 28)-Net over F₂₅ — Constructive and digital

Digital (2, 21, 28)-net over F₂₅, using

net from sequence [i] based on digital (2, 27)-sequence over F₂₅, using
- Niederreiter sequence [i]

(21−19, 21, 46)-Net over F₂₅ — Digital

Digital (2, 21, 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]

(21−19, 21, 215)-Net in Base 25 — Upper bound on s

There is no (2, 21, 216)-net in base 25, because

3 times m-reduction [i] would yield (2, 18, 216)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 14 881355 721034 799302 301185 > 25¹⁸ [i]