MinT - Best Known (55, 55+52, s)-Nets in Base 16

Best Known (55, 55+52, s)-Nets in Base 16

(55, 55+52, 516)-Net over F₁₆ — Constructive and digital

Digital (55, 107, 516)-net over F₁₆, using

1 times m-reduction [i] based on digital (55, 108, 516)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 54, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(55, 55+52, 578)-Net over F₁₆ — Digital

Digital (55, 107, 578)-net over F₁₆, using

1 times m-reduction [i] based on digital (55, 108, 578)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 54, 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]

(55, 55+52, 63463)-Net in Base 16 — Upper bound on s

There is no (55, 107, 63464)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 693 424498 030578 190419 485827 681116 895473 510814 317401 137371 347919 217461 912475 445570 355759 359052 613945 357840 730735 941768 234183 397836 > 16¹⁰⁷ [i]