MinT - Best Known (71−63, 71, s)-Nets in Base 64

Best Known (71−63, 71, s)-Nets in Base 64

(71−63, 71, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 71, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 71, 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]

(71−63, 71, 2345)-Net in Base 64 — Upper bound on s

There is no (8, 71, 2346)-net in base 64, because

1 times m-reduction [i] would yield (8, 70, 2346)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2 711451 679283 955483 973714 870102 535493 973090 019820 710350 198586 833781 359606 722508 227386 154252 970591 222399 183083 695077 066835 898352 > 64⁷⁰ [i]