MinT - Best Known (62−28, 62, s)-Nets in Base 16

Best Known (62−28, 62, s)-Nets in Base 16

(62−28, 62, 520)-Net over F₁₆ — Constructive and digital

Digital (34, 62, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 31, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(62−28, 62, 642)-Net over F₁₆ — Digital

Digital (34, 62, 642)-net over F₁₆, using

2 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]

(62−28, 62, 86668)-Net in Base 16 — Upper bound on s

There is no (34, 62, 86669)-net in base 16, because

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]