MinT - Best Known (27, 27+23, s)-Nets in Base 16

Best Known (27, 27+23, s)-Nets in Base 16

(27, 27+23, 518)-Net over F₁₆ — Constructive and digital

Digital (27, 50, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 25, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(27, 27+23, 642)-Net over F₁₆ — Digital

Digital (27, 50, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 25, 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]

(27, 27+23, 75630)-Net in Base 16 — Upper bound on s

There is no (27, 50, 75631)-net in base 16, because

1 times m-reduction [i] would yield (27, 49, 75631)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 100440 421559 188871 050229 337036 028398 259757 443289 696997 152116 > 16⁴⁹ [i]