MinT - Best Known (82−39, 82, s)-Nets in Base 16

Best Known (82−39, 82, s)-Nets in Base 16

(82−39, 82, 518)-Net over F₁₆ — Constructive and digital

Digital (43, 82, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 41, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(82−39, 82, 642)-Net over F₁₆ — Digital

Digital (43, 82, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 41, 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]

(82−39, 82, 71848)-Net in Base 16 — Upper bound on s

There is no (43, 82, 71849)-net in base 16, because

1 times m-reduction [i] would yield (43, 81, 71849)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 34 183151 023454 363456 237363 591010 325912 884006 443218 491547 887792 658755 393253 964485 682692 470100 303216 > 16⁸¹ [i]