MinT - Best Known (103−49, 103, s)-Nets in Base 16

Best Known (103−49, 103, s)-Nets in Base 16

(103−49, 103, 518)-Net over F₁₆ — Constructive and digital

Digital (54, 103, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (54, 104, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 52, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(103−49, 103, 642)-Net over F₁₆ — Digital

Digital (54, 103, 642)-net over F₁₆, using

1 times m-reduction [i] based on digital (54, 104, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 52, 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]

(103−49, 103, 85647)-Net in Base 16 — Upper bound on s

There is no (54, 103, 85648)-net in base 16, because

1 times m-reduction [i] would yield (54, 102, 85648)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 661 137838 112332 866414 939544 601948 053995 371672 453471 135248 584282 294917 082909 734366 802554 499721 193976 761644 114678 590209 007256 > 16¹⁰² [i]