MinT - Best Known (8, 24, s)-Nets in Base 64

Best Known (8, 24, s)-Nets in Base 64

(8, 24, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 24, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 24, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(8, 24, 259)-Net in Base 64 — Constructive

(8, 24, 259)-net in base 64, using

base change [i] based on digital (2, 18, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(8, 24, 321)-Net in Base 64

(8, 24, 321)-net in base 64, using

base change [i] based on digital (2, 18, 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]

(8, 24, 15659)-Net in Base 64 — Upper bound on s

There is no (8, 24, 15660)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 22 301931 957999 865635 259745 785210 861813 503457 > 64²⁴ [i]