MinT - Best Known (16, 16+70, s)-Nets in Base 64

Best Known (16, 16+70, s)-Nets in Base 64

(16, 16+70, 177)-Net over F₆₄ — Constructive and digital

Digital (16, 86, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 86, 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]

(16, 16+70, 192)-Net in Base 64 — Constructive

(16, 86, 192)-net in base 64, using

5 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
- base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(16, 16+70, 267)-Net over F₆₄ — Digital

Digital (16, 86, 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]

(16, 16+70, 6035)-Net in Base 64 — Upper bound on s

There is no (16, 86, 6036)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 215293 090007 019433 125656 745699 270399 376441 056650 849032 100363 335712 068771 482132 315014 542655 492251 628214 845381 658676 794578 351749 571607 427994 071686 195697 912276 > 64⁸⁶ [i]