MinT - Best Known (63−29, 63, s)-Nets in Base 16

Best Known (63−29, 63, s)-Nets in Base 16

(63−29, 63, 518)-Net over F₁₆ — Constructive and digital

Digital (34, 63, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (34, 64, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 32, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(63−29, 63, 642)-Net over F₁₆ — Digital

Digital (34, 63, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (34, 64, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 32, 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]

(63−29, 63, 86668)-Net in Base 16 — Upper bound on s

There is no (34, 63, 86669)-net in base 16, because

1 times m-reduction [i] would yield (34, 62, 86669)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 452 359497 405739 290418 792796 352728 693215 661313 697134 549170 751619 111731 447616 > 16⁶² [i]