MinT - Best Known (89−42, 89, s)-Nets in Base 16

Best Known (89−42, 89, s)-Nets in Base 16

(89−42, 89, 518)-Net over F₁₆ — Constructive and digital

Digital (47, 89, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (47, 90, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 45, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(89−42, 89, 642)-Net over F₁₆ — Digital

Digital (47, 89, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (47, 90, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 45, 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]

(89−42, 89, 73368)-Net in Base 16 — Upper bound on s

There is no (47, 89, 73369)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 146809 460503 858666 611073 367078 332975 499368 937505 922668 100627 613604 830694 898598 984316 411390 006844 084473 663736 > 16⁸⁹ [i]