MinT - Best Known (17, 68, s)-Nets in Base 64

Best Known (17, 68, s)-Nets in Base 64

(17, 68, 177)-Net over F₆₄ — Constructive and digital

Digital (17, 68, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 68, 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]

(17, 68, 257)-Net in Base 64 — Constructive

(17, 68, 257)-net in base 64, using

base change [i] based on digital (0, 51, 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]

(17, 68, 267)-Net over F₆₄ — Digital

Digital (17, 68, 267)-net over F₆₄, using

t-expansion [i] based on digital (16, 68, 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]

(17, 68, 11178)-Net in Base 64 — Upper bound on s

There is no (17, 68, 11179)-net in base 64, because

1 times m-reduction [i] would yield (17, 67, 11179)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 10 350772 565610 976753 663744 928425 430949 076819 395442 610335 764215 495391 499538 173140 487711 773565 591310 523543 857549 744730 480220 > 64⁶⁷ [i]