MinT - Best Known (89−79, 89, s)-Nets in Base 64

Best Known (89−79, 89, s)-Nets in Base 64

(89−79, 89, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 89, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 89, 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]

(89−79, 89, 225)-Net over F₆₄ — Digital

Digital (10, 89, 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]

(89−79, 89, 2888)-Net in Base 64 — Upper bound on s

There is no (10, 89, 2889)-net in base 64, because

1 times m-reduction [i] would yield (10, 88, 2889)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 887 835784 674876 456617 977326 422252 218506 566201 271555 541376 820702 982719 673151 953348 689498 585124 182892 636549 815727 469490 799460 911292 132139 784067 725617 157133 258128 > 64⁸⁸ [i]