MinT - Best Known (26, 47, s)-Nets in Base 16

Best Known (26, 47, s)-Nets in Base 16

(26, 47, 518)-Net over F₁₆ — Constructive and digital

Digital (26, 47, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (26, 48, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 24, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(26, 47, 642)-Net over F₁₆ — Digital

Digital (26, 47, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (26, 48, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 24, 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]

(26, 47, 104427)-Net in Base 16 — Upper bound on s

There is no (26, 47, 104428)-net in base 16, because

1 times m-reduction [i] would yield (26, 46, 104428)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 24 520765 576575 495909 184887 397660 850570 727194 328604 924951 > 16⁴⁶ [i]