MinT - Best Known (91−67, 91, s)-Nets in Base 64

Best Known (91−67, 91, s)-Nets in Base 64

(91−67, 91, 177)-Net over F₆₄ — Constructive and digital

Digital (24, 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]

(91−67, 91, 288)-Net in Base 64 — Constructive

(24, 91, 288)-net in base 64, using

t-expansion [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(91−67, 91, 342)-Net over F₆₄ — Digital

Digital (24, 91, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 91, 342)-net over F₆₄, using
- net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
    - a curve from the manYPoints database [i]

(91−67, 91, 17601)-Net in Base 64 — Upper bound on s

There is no (24, 91, 17602)-net in base 64, because

1 times m-reduction [i] would yield (24, 90, 17602)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 602002 771784 700372 240074 235506 078500 285968 581659 694251 627389 979764 615246 094335 277424 747864 041900 099235 191799 752934 281288 269604 089936 928373 046024 091525 165500 381022 > 64⁹⁰ [i]