MinT - Best Known (51, 51+48, s)-Nets in Base 16

Best Known (51, 51+48, s)-Nets in Base 16

(51, 51+48, 516)-Net over F₁₆ — Constructive and digital

Digital (51, 99, 516)-net over F₁₆, using

1 times m-reduction [i] based on digital (51, 100, 516)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 50, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(51, 51+48, 578)-Net over F₁₆ — Digital

Digital (51, 99, 578)-net over F₁₆, using

1 times m-reduction [i] based on digital (51, 100, 578)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 50, 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]

(51, 51+48, 60558)-Net in Base 16 — Upper bound on s

There is no (51, 99, 60559)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 161446 100354 573895 708555 108213 158031 061149 691489 162815 640947 693899 174783 880042 177118 099614 274646 585649 526179 434463 642616 > 16⁹⁹ [i]