MinT - Best Known (60−45, 60, s)-Nets in Base 64

Best Known (60−45, 60, s)-Nets in Base 64

(60−45, 60, 177)-Net over F₆₄ — Constructive and digital

Digital (15, 60, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 60, 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]

(60−45, 60, 257)-Net in Base 64 — Constructive

(15, 60, 257)-net in base 64, using

base change [i] based on digital (0, 45, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(60−45, 60, 258)-Net over F₆₄ — Digital

Digital (15, 60, 258)-net over F₆₄, using

net from sequence [i] based on digital (15, 257)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 15 and N(F) ≥ 258, using
  - a curve from the manYPoints database [i]

(60−45, 60, 10020)-Net in Base 64 — Upper bound on s

There is no (15, 60, 10021)-net in base 64, because

1 times m-reduction [i] would yield (15, 59, 10021)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 36737 122060 882410 149388 598616 946965 551658 448189 360430 688661 736052 278148 719736 949685 307811 009463 090225 446256 > 64⁵⁹ [i]