MinT - Best Known (55, 55+47, s)-Nets in Base 16

Best Known (55, 55+47, s)-Nets in Base 16

(55, 55+47, 522)-Net over F₁₆ — Constructive and digital

Digital (55, 102, 522)-net over F₁₆, using

trace code for nets [i] based on digital (4, 51, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(55, 55+47, 642)-Net over F₁₆ — Digital

Digital (55, 102, 642)-net over F₁₆, using

4 times m-reduction [i] based on digital (55, 106, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 53, 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]

(55, 55+47, 121892)-Net in Base 16 — Upper bound on s

There is no (55, 102, 121893)-net in base 16, because

1 times m-reduction [i] would yield (55, 101, 121893)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 41 318365 802178 835847 002564 098971 411723 601518 708464 694056 437210 165601 039358 912575 187626 917529 459158 010687 517584 342960 719136 > 16¹⁰¹ [i]