MinT - Best Known (3, 22, s)-Nets in Base 64

Best Known (3, 22, s)-Nets in Base 64

(3, 22, 104)-Net over F₆₄ — Constructive and digital

Digital (3, 22, 104)-net over F₆₄, using

net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
  - a function field by SÃ©mirat [i]

(3, 22, 113)-Net over F₆₄ — Digital

Digital (3, 22, 113)-net over F₆₄, using

net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(3, 22, 1074)-Net in Base 64 — Upper bound on s

There is no (3, 22, 1075)-net in base 64, because

1 times m-reduction [i] would yield (3, 21, 1075)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 85 506522 544753 941398 768584 065436 359196 > 64²¹ [i]