MinT - Best Known (49−47, 49, s)-Nets in Base 25

Best Known (49−47, 49, s)-Nets in Base 25

(49−47, 49, 28)-Net over F₂₅ — Constructive and digital

Digital (2, 49, 28)-net over F₂₅, using

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

(49−47, 49, 46)-Net over F₂₅ — Digital

Digital (2, 49, 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]

(49−47, 49, 186)-Net in Base 25 — Upper bound on s

There is no (2, 49, 187)-net in base 25, because

4 times m-reduction [i] would yield (2, 45, 187)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(25⁴⁵, 187, S₂₅, 43), but
  - the linear programming bound shows that MÂ â‰¥ 111 488601 007381 568900 361473 791104 508011 644280 696117 448314 907960 593700 408935 546875 / 137824 248946 330259 > 25⁴⁵ [i]