MinT - Best Known (88−73, 88, s)-Nets in Base 64

Best Known (88−73, 88, s)-Nets in Base 64

(88−73, 88, 177)-Net over F₆₄ — Constructive and digital

Digital (15, 88, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 88, 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]

(88−73, 88, 258)-Net over F₆₄ — Digital

Digital (15, 88, 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]

(88−73, 88, 5234)-Net in Base 64 — Upper bound on s

There is no (15, 88, 5235)-net in base 64, because

1 times m-reduction [i] would yield (15, 87, 5235)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 13 821887 001171 200833 233478 641319 638963 814223 494250 984903 181738 110072 404427 671602 203624 299003 931192 167123 665258 942232 161484 599446 655207 056482 667261 176446 497860 > 64⁸⁷ [i]