MinT - Best Known (16, 83, s)-Nets in Base 64

Best Known (16, 83, s)-Nets in Base 64

(16, 83, 177)-Net over F₆₄ — Constructive and digital

Digital (16, 83, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 83, 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, 83, 192)-Net in Base 64 — Constructive

(16, 83, 192)-net in base 64, using

8 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
- base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(16, 83, 267)-Net over F₆₄ — Digital

Digital (16, 83, 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, 83, 6411)-Net in Base 64 — Upper bound on s

There is no (16, 83, 6412)-net in base 64, because

1 times m-reduction [i] would yield (16, 82, 6412)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 12799 860856 896916 006462 652430 361160 706042 932413 449577 493277 329056 629186 642463 728217 332605 123118 594960 071829 414940 667454 670499 893278 044786 531667 866680 > 64⁸² [i]