MinT - Best Known (80−71, 80, s)-Nets in Base 64

Best Known (80−71, 80, s)-Nets in Base 64

(80−71, 80, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 80, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 80, 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]

(80−71, 80, 209)-Net over F₆₄ — Digital

Digital (9, 80, 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]

(80−71, 80, 2617)-Net in Base 64 — Upper bound on s

There is no (9, 80, 2618)-net in base 64, because

1 times m-reduction [i] would yield (9, 79, 2618)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 49326 489156 523978 114017 118791 838869 343166 846421 718196 586909 937840 981326 334794 584450 672242 600317 336770 113653 507022 917212 434913 986439 954994 351340 > 64⁷⁹ [i]