MinT - Best Known (10, 10+65, s)-Nets in Base 64

Best Known (10, 10+65, s)-Nets in Base 64

(10, 10+65, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 75, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 75, 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]

(10, 10+65, 225)-Net over F₆₄ — Digital

Digital (10, 75, 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]

(10, 10+65, 3034)-Net in Base 64 — Upper bound on s

There is no (10, 75, 3035)-net in base 64, because

1 times m-reduction [i] would yield (10, 74, 3035)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 45 797006 615683 078697 573597 241021 941977 212072 245383 657672 332894 332349 118583 081158 747118 216536 729458 457395 229059 183992 314716 008712 865654 > 64⁷⁴ [i]