MinT - Best Known (21, 21+17, s)-Nets in Base 16

Best Known (21, 21+17, s)-Nets in Base 16

(21, 21+17, 518)-Net over F₁₆ — Constructive and digital

Digital (21, 38, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 19, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(21, 21+17, 642)-Net over F₁₆ — Digital

Digital (21, 38, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 19, 321)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(21, 21+17, 93032)-Net in Base 16 — Upper bound on s

There is no (21, 38, 93033)-net in base 16, because

1 times m-reduction [i] would yield (21, 37, 93033)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 356 825905 122096 883361 627910 949522 836771 028261 > 16³⁷ [i]