MinT - Best Known (16, 77, s)-Nets in Base 64

Best Known (16, 77, s)-Nets in Base 64

(16, 77, 177)-Net over F₆₄ — Constructive and digital

Digital (16, 77, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 77, 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]

(16, 77, 216)-Net in Base 64 — Constructive

(16, 77, 216)-net in base 64, using

base change [i] based on digital (5, 66, 216)-net over F₁₂₈, using
- net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
    - a function field by SÃ©mirat [i]

(16, 77, 267)-Net over F₆₄ — Digital

Digital (16, 77, 267)-net over F₆₄, using

net from sequence [i] based on digital (16, 266)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 16 and N(F) ≥ 267, using
  - a curve from the manYPoints database [i]

(16, 77, 7181)-Net in Base 64 — Upper bound on s

There is no (16, 77, 7182)-net in base 64, because

1 times m-reduction [i] would yield (16, 76, 7182)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 186658 255333 570733 594278 551986 104838 114576 083776 789368 287031 177280 070473 819408 174783 641251 230181 774192 192904 031309 605776 975055 532370 531840 > 64⁷⁶ [i]