MinT - Best Known (15, 15+71, s)-Nets in Base 64

Best Known (15, 15+71, s)-Nets in Base 64

(15, 15+71, 177)-Net over F₆₄ — Constructive and digital

Digital (15, 86, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 86, 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]

(15, 15+71, 258)-Net over F₆₄ — Digital

Digital (15, 86, 258)-net over F₆₄, using

net from sequence [i] based on digital (15, 257)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 15 and N(F) ≥ 258, using
  - a curve from the manYPoints database [i]

(15, 15+71, 5357)-Net in Base 64 — Upper bound on s

There is no (15, 86, 5358)-net in base 64, because

1 times m-reduction [i] would yield (15, 85, 5358)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3368 775961 802581 042923 975662 740508 054594 325101 597236 149733 336617 404096 413007 811198 544813 188911 234228 544962 303827 474345 034529 058419 483316 927797 919534 463950 > 64⁸⁵ [i]