MinT - Best Known (56, 56+52, s)-Nets in Base 16

Best Known (56, 56+52, s)-Nets in Base 16

(56, 56+52, 518)-Net over F₁₆ — Constructive and digital

Digital (56, 108, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 54, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(56, 56+52, 642)-Net over F₁₆ — Digital

Digital (56, 108, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 54, 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]

(56, 56+52, 70606)-Net in Base 16 — Upper bound on s

There is no (56, 108, 70607)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11093 570212 614137 093666 619754 791103 029321 255007 578775 482402 370039 029833 353149 092703 517018 816499 831045 278251 700263 242500 355580 137356 > 16¹⁰⁸ [i]