MinT - Best Known (25, 25+21, s)-Nets in Base 16

Best Known (25, 25+21, s)-Nets in Base 16

(25, 25+21, 518)-Net over F₁₆ — Constructive and digital

Digital (25, 46, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 23, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(25, 25+21, 642)-Net over F₁₆ — Digital

Digital (25, 46, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 23, 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]

(25, 25+21, 79140)-Net in Base 16 — Upper bound on s

There is no (25, 46, 79141)-net in base 16, because

1 times m-reduction [i] would yield (25, 45, 79141)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 532669 112464 792637 538217 916750 166826 562938 162433 668776 > 16⁴⁵ [i]