MinT - Best Known (5, 44, s)-Nets in Base 64

Best Known (5, 44, s)-Nets in Base 64

(5, 44, 128)-Net over F₆₄ — Constructive and digital

Digital (5, 44, 128)-net over F₆₄, using

net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
  - a function field by SÃ©mirat [i]

(5, 44, 133)-Net over F₆₄ — Digital

Digital (5, 44, 133)-net over F₆₄, using

net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
  - a curve from the manYPoints database [i]

(5, 44, 1530)-Net in Base 64 — Upper bound on s

There is no (5, 44, 1531)-net in base 64, because

1 times m-reduction [i] would yield (5, 43, 1531)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 464326 628427 244183 308832 949337 224818 087268 809004 455148 569436 228980 176078 011848 > 64⁴³ [i]