MinT - Best Known (3, 48, s)-Nets in Base 25

Best Known (3, 48, s)-Nets in Base 25

(3, 48, 52)-Net over F₂₅ — Constructive and digital

Digital (3, 48, 52)-net over F₂₅, using

net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
  - a function field by GarcÃa and Quoos [i]

(3, 48, 56)-Net over F₂₅ — Digital

Digital (3, 48, 56)-net over F₂₅, using

net from sequence [i] based on digital (3, 55)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 56, using
  - fields by Serre with genus 3 or 4 [i]

(3, 48, 275)-Net in Base 25 — Upper bound on s

There is no (3, 48, 276)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁴⁸, 276, S₂₅, 45), but
- the linear programming bound shows that MÂ â‰¥ 3307 138010 174822 388535 580256 075747 109220 233429 320557 304309 513568 796319 304965 436458 587646 484375 / 256 170211 214124 669369 575029 > 25⁴⁸ [i]