MinT - Best Known (105−50, 105, s)-Nets in Base 16

Best Known (105−50, 105, s)-Nets in Base 16

(105−50, 105, 518)-Net over F₁₆ — Constructive and digital

Digital (55, 105, 518)-net over F₁₆, using

1 times m-reduction [i] based on digital (55, 106, 518)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 53, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(105−50, 105, 642)-Net over F₁₆ — Digital

Digital (55, 105, 642)-net over F₁₆, using

1 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]

(105−50, 105, 77403)-Net in Base 16 — Upper bound on s

There is no (55, 105, 77404)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 707931 382429 087324 394150 247703 762935 469406 319878 707254 752071 381249 451984 354388 942472 864631 202660 816106 037938 540931 557046 576501 > 16¹⁰⁵ [i]