MinT - Best Known (68, 68+62, s)-Nets in Base 16

Best Known (68, 68+62, s)-Nets in Base 16

(68, 68+62, 520)-Net over F₁₆ — Constructive and digital

Digital (68, 130, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 65, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(68, 68+62, 642)-Net over F₁₆ — Digital

Digital (68, 130, 642)-net over F₁₆, using

t-expansion [i] based on digital (67, 130, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 65, 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]

(68, 68+62, 92767)-Net in Base 16 — Upper bound on s

There is no (68, 130, 92768)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 432636 021935 126876 278539 341953 345063 102685 777614 756982 400498 113224 852175 399392 338305 375418 937574 834819 409243 966916 871598 899760 162877 365475 103897 969649 437371 > 16¹³⁰ [i]