MinT - Best Known (20, 20+63, s)-Nets in Base 64

Best Known (20, 20+63, s)-Nets in Base 64

(20, 20+63, 177)-Net over F₆₄ — Constructive and digital

Digital (20, 83, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 83, 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]

(20, 20+63, 216)-Net in Base 64 — Constructive

(20, 83, 216)-net in base 64, using

t-expansion [i] based on (18, 83, 216)-net in base 64, using
- 8 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
  - base change [i] based on digital (5, 78, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(20, 20+63, 342)-Net over F₆₄ — Digital

Digital (20, 83, 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]

(20, 20+63, 11796)-Net in Base 64 — Upper bound on s

There is no (20, 83, 11797)-net in base 64, because

1 times m-reduction [i] would yield (20, 82, 11797)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 12797 292708 120316 572612 768416 523585 789123 561993 111524 026184 379251 820845 600525 313244 625879 648249 937661 816568 679369 803100 801655 223968 956217 623661 003264 > 64⁸² [i]