MinT - Best Known (99−96, 99, s)-Nets in Base 25

Best Known (99−96, 99, s)-Nets in Base 25

(99−96, 99, 52)-Net over F₂₅ — Constructive and digital

Digital (3, 99, 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]

(99−96, 99, 56)-Net over F₂₅ — Digital

Digital (3, 99, 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]

(99−96, 99, 95)-Net in Base 25 — Upper bound on s

There is no (3, 99, 96)-net in base 25, because

9 times m-reduction [i] would yield (3, 90, 96)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(25⁹⁰, 96, S₂₅, 87), but
  - the linear programming bound shows that MÂ â‰¥ 13 668865 221078 739256 015071 809629 879850 936124 576679 322503 501034 318504 064092 312472 780759 593604 486823 448240 784273 366443 812847 137451 171875 / 20 559539 > 25⁹⁰ [i]