MinT - Best Known (43−19, 43, s)-Nets in Base 16

Best Known (43−19, 43, s)-Nets in Base 16

(43−19, 43, 518)-Net over F₁₆ — Constructive and digital

Digital (24, 43, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (24, 44, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 22, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(43−19, 43, 642)-Net over F₁₆ — Digital

Digital (24, 43, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (24, 44, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 22, 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]

(43−19, 43, 115045)-Net in Base 16 — Upper bound on s

There is no (24, 43, 115046)-net in base 16, because

1 times m-reduction [i] would yield (24, 42, 115046)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 374 160802 148838 276075 206288 518567 327690 308786 816436 > 16⁴² [i]