MinT - Best Known (2, 2+38, s)-Nets in Base 25

Best Known (2, 2+38, s)-Nets in Base 25

(2, 2+38, 28)-Net over F₂₅ — Constructive and digital

Digital (2, 40, 28)-net over F₂₅, using

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

(2, 2+38, 46)-Net over F₂₅ — Digital

Digital (2, 40, 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]

(2, 2+38, 191)-Net in Base 25 — Upper bound on s

There is no (2, 40, 192)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁴⁰, 192, S₂₅, 38), but
- the linear programming bound shows that MÂ â‰¥ 456 191186 460861 513045 184981 377639 342470 242667 104685 097001 492977 142333 984375 / 5 324411 907884 504503 > 25⁴⁰ [i]