MinT - Best Known (55, 55+49, s)-Nets in Base 16

Best Known (55, 55+49, s)-Nets in Base 16

(55, 55+49, 520)-Net over F₁₆ — Constructive and digital

Digital (55, 104, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 52, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(55, 55+49, 642)-Net over F₁₆ — Digital

Digital (55, 104, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (55, 106, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 53, 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]

(55, 55+49, 96137)-Net in Base 16 — Upper bound on s

There is no (55, 104, 96138)-net in base 16, because

1 times m-reduction [i] would yield (55, 103, 96138)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10577 588503 769628 796910 164580 959692 255703 627459 686382 732657 006635 182852 186753 238826 365335 761425 634362 283350 714438 198253 337656 > 16¹⁰³ [i]