MinT - Best Known (5−4, 5, s)-Nets in Base 25

Best Known (5−4, 5, s)-Nets in Base 25

(5−4, 5, 27)-Net over F₂₅ — Constructive and digital

Digital (1, 5, 27)-net over F₂₅, using

net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
- Niederreiter sequence [i]

(5−4, 5, 36)-Net over F₂₅ — Digital

Digital (1, 5, 36)-net over F₂₅, using

net from sequence [i] based on digital (1, 35)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 1 and N(F) ≥ 36, using
  - sharp bound on the number of rational points on curves with genus 1 [i]

(5−4, 5, 181)-Net in Base 25 — Upper bound on s

There is no (1, 5, 182)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁵, 182, S₂₅, 4), but
- the linear programming bound shows that MÂ â‰¥ 1 005484 453125 / 102709 > 25⁵ [i]