MinT - Best Known (81−71, 81, s)-Nets in Base 64

Best Known (81−71, 81, s)-Nets in Base 64

(81−71, 81, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 81, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 81, 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]

(81−71, 81, 225)-Net over F₆₄ — Digital

Digital (10, 81, 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]

(81−71, 81, 2949)-Net in Base 64 — Upper bound on s

There is no (10, 81, 2950)-net in base 64, because

1 times m-reduction [i] would yield (10, 80, 2950)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 137199 155500 174731 995843 414590 023916 802879 648835 846913 796726 977027 486358 483660 862619 970942 475235 243423 134781 087614 690929 272522 630189 585408 254040 > 64⁸⁰ [i]