MinT - Best Known (21, 21+34, s)-Nets in Base 64

Best Known (21, 21+34, s)-Nets in Base 64

(21, 21+34, 184)-Net over F₆₄ — Constructive and digital

Digital (21, 55, 184)-net over F₆₄, using

(u,Â u+v)-construction [i] based on
1. digital (1, 18, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]
2. digital (3, 37, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(21, 21+34, 288)-Net in Base 64 — Constructive

(21, 55, 288)-net in base 64, using

29 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(21, 21+34, 342)-Net over F₆₄ — Digital

Digital (21, 55, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 55, 342)-net over F₆₄, using
- net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
    - a curve from the manYPoints database [i]

(21, 21+34, 79447)-Net in Base 64 — Upper bound on s

There is no (21, 55, 79448)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2187 256653 369026 307616 414347 233051 738634 271277 181255 680921 568185 348069 215264 736824 976352 065045 011273 > 64⁵⁵ [i]