MinT - Best Known (48−22, 48, s)-Nets in Base 16

Best Known (48−22, 48, s)-Nets in Base 16

(48−22, 48, 518)-Net over F₁₆ — Constructive and digital

Digital (26, 48, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 24, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(48−22, 48, 642)-Net over F₁₆ — Digital

Digital (26, 48, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 24, 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]

(48−22, 48, 58779)-Net in Base 16 — Upper bound on s

There is no (26, 48, 58780)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6278 262384 980538 882642 457078 644635 676015 709278 091854 556201 > 16⁴⁸ [i]