MinT - Best Known (9, 9+82, s)-Nets in Base 64

Best Known (9, 9+82, s)-Nets in Base 64

(9, 9+82, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 91, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 91, 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]

(9, 9+82, 209)-Net over F₆₄ — Digital

Digital (9, 91, 209)-net over F₆₄, using

net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
  - a curve from the manYPoints database [i]

(9, 9+82, 2593)-Net in Base 64 — Upper bound on s

There is no (9, 91, 2594)-net in base 64, because

2 times m-reduction [i] would yield (9, 89, 2594)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56871 629358 755027 837595 199195 900619 250061 794558 164966 208783 048022 779582 893229 756197 014384 876664 660879 870684 484147 016361 849506 132893 688501 430714 490122 782649 154496 > 64⁸⁹ [i]