MinT - Best Known (2, 2+11, s)-Nets in Base 25

Best Known (2, 2+11, s)-Nets in Base 25

(2, 2+11, 28)-Net over F₂₅ — Constructive and digital

Digital (2, 13, 28)-net over F₂₅, using

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

(2, 2+11, 46)-Net over F₂₅ — Digital

Digital (2, 13, 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+11, 243)-Net in Base 25 — Upper bound on s

There is no (2, 13, 244)-net in base 25, because

1 times m-reduction [i] would yield (2, 12, 244)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 60025 723085 725537 > 25¹² [i]
- extracting embedded orthogonal array [i] would yield OA(25¹², 244, S₂₅, 10), but
  - the linear programming bound shows that MÂ â‰¥ 5 197276 439112 292423 248291 015625 / 86 772815 851171 > 25¹² [i]