MinT - Best Known (10, 38, s)-Nets in Base 64

Best Known (10, 38, s)-Nets in Base 64

(10, 38, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 38, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 38, 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]

(10, 38, 225)-Net over F₆₄ — Digital

Digital (10, 38, 225)-net over F₆₄, using

net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
  - a curve from the manYPoints database [i]

(10, 38, 257)-Net in Base 64 — Constructive

(10, 38, 257)-net in base 64, using

2 times m-reduction [i] based on (10, 40, 257)-net in base 64, using
- base change [i] based on digital (0, 30, 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]

(10, 38, 7659)-Net in Base 64 — Upper bound on s

There is no (10, 38, 7660)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 431 414308 460318 993035 844473 205637 046456 784483 934919 072892 224199 442520 > 64³⁸ [i]