MinT - Best Known (17−15, 17, s)-Nets in Base 25

Best Known (17−15, 17, s)-Nets in Base 25

(17−15, 17, 28)-Net over F₂₅ — Constructive and digital

Digital (2, 17, 28)-net over F₂₅, using

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

(17−15, 17, 46)-Net over F₂₅ — Digital

Digital (2, 17, 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]

(17−15, 17, 215)-Net in Base 25 — Upper bound on s

There is no (2, 17, 216)-net in base 25, because

1 times m-reduction [i] would yield (2, 16, 216)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(25¹⁶, 216, S₂₅, 14), but
  - the linear programming bound shows that MÂ â‰¥ 12 448694 004708 523858 263947 069644 927978 515625 / 519 959667 166403 739577 > 25¹⁶ [i]