MinT - Best Known (21, 21+70, s)-Nets in Base 64

Best Known (21, 21+70, s)-Nets in Base 64

(21, 21+70, 177)-Net over F₆₄ — Constructive and digital

Digital (21, 91, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 91, 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]

(21, 21+70, 216)-Net in Base 64 — Constructive

(21, 91, 216)-net in base 64, using

t-expansion [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]

(21, 21+70, 342)-Net over F₆₄ — Digital

Digital (21, 91, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 91, 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+70, 10947)-Net in Base 64 — Upper bound on s

There is no (21, 91, 10948)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 231 074119 875929 291696 859016 723021 667654 273884 127365 486025 846939 752001 403671 640138 331204 248131 828461 871619 986400 483961 647053 588001 526150 230825 165459 432452 630282 181550 > 64⁹¹ [i]