MinT - Best Known (1, 1+6, s)-Nets in Base 25

Best Known (1, 1+6, s)-Nets in Base 25

(1, 1+6, 27)-Net over F₂₅ — Constructive and digital

Digital (1, 7, 27)-net over F₂₅, using

net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
- Niederreiter sequence [i]

(1, 1+6, 36)-Net over F₂₅ — Digital

Digital (1, 7, 36)-net over F₂₅, using

net from sequence [i] based on digital (1, 35)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 1 and N(F) ≥ 36, using
  - sharp bound on the number of rational points on curves with genus 1 [i]

(1, 1+6, 134)-Net in Base 25 — Upper bound on s

There is no (1, 7, 135)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁷, 135, S₂₅, 6), but
- the linear programming bound shows that MÂ â‰¥ 9522 358398 437500 / 1 515061 > 25⁷ [i]