MinT - Best Known (1, 1+5, s)-Nets in Base 16

Best Known (1, 1+5, s)-Nets in Base 16

(1, 1+5, 24)-Net over F₁₆ — Constructive and digital

Digital (1, 6, 24)-net over F₁₆, using

net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
  - a function field by SÃ©mirat [i]

(1, 1+5, 25)-Net over F₁₆ — Digital

Digital (1, 6, 25)-net over F₁₆, using

net from sequence [i] based on digital (1, 24)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 25, using
  - sharp bound on the number of rational points on curves with genus 1 [i]

(1, 1+5, 93)-Net in Base 16 — Upper bound on s

There is no (1, 6, 94)-net in base 16, because

1 times m-reduction [i] would yield (1, 5, 94)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16⁵, 94, S₁₆, 4), but
  - the linear programming bound shows that MÂ â‰¥ 2179 760128 / 2071 > 16⁵ [i]