MinT - Best Known (112−54, 112, s)-Nets in Base 16

Best Known (112−54, 112, s)-Nets in Base 16

(112−54, 112, 518)-Net over F₁₆ — Constructive and digital

Digital (58, 112, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 56, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(112−54, 112, 642)-Net over F₁₆ — Digital

Digital (58, 112, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 56, 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]

(112−54, 112, 71960)-Net in Base 16 — Upper bound on s

There is no (58, 112, 71961)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 726 970180 778745 191679 044113 269175 116320 182423 514421 621751 033439 963100 935209 804511 098417 919300 729935 274063 795949 323286 920150 834355 149056 > 16¹¹² [i]