MinT - Best Known (74−58, 74, s)-Nets in Base 64

Best Known (74−58, 74, s)-Nets in Base 64

(74−58, 74, 177)-Net over F₆₄ — Constructive and digital

Digital (16, 74, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 74, 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]

(74−58, 74, 216)-Net in Base 64 — Constructive

(16, 74, 216)-net in base 64, using

3 times m-reduction [i] based on (16, 77, 216)-net in base 64, using
- base change [i] based on digital (5, 66, 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]

(74−58, 74, 267)-Net over F₆₄ — Digital

Digital (16, 74, 267)-net over F₆₄, using

net from sequence [i] based on digital (16, 266)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 16 and N(F) ≥ 267, using
  - a curve from the manYPoints database [i]

(74−58, 74, 7513)-Net in Base 64 — Upper bound on s

There is no (16, 74, 7514)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 45 583396 824734 567369 930693 280544 246688 577893 861831 007736 024124 946738 839984 340767 316457 026232 680994 373162 102677 062715 230939 802105 486576 > 64⁷⁴ [i]