MinT - Best Known (38−36, 38, s)-Nets in Base 25

Best Known (38−36, 38, s)-Nets in Base 25

(38−36, 38, 28)-Net over F₂₅ — Constructive and digital

Digital (2, 38, 28)-net over F₂₅, using

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

(38−36, 38, 46)-Net over F₂₅ — Digital

Digital (2, 38, 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]

(38−36, 38, 196)-Net in Base 25 — Upper bound on s

There is no (2, 38, 197)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25³⁸, 197, S₂₅, 36), but
- the linear programming bound shows that MÂ â‰¥ 5444 189784 131503 251842 998055 733124 918020 848781 452514 231204 986572 265625 / 40820 999541 573793 > 25³⁸ [i]