MinT - Best Known (106−52, 106, s)-Nets in Base 16

Best Known (106−52, 106, s)-Nets in Base 16

(106−52, 106, 516)-Net over F₁₆ — Constructive and digital

Digital (54, 106, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 53, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(106−52, 106, 578)-Net over F₁₆ — Digital

Digital (54, 106, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 53, 289)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(106−52, 106, 57042)-Net in Base 16 — Upper bound on s

There is no (54, 106, 57043)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 43 334318 378509 397281 807571 913414 584510 938621 957316 986963 959649 281909 257570 883289 785146 723942 967872 743377 367559 935782 570084 719896 > 16¹⁰⁶ [i]