MinT - Best Known (78−56, 78, s)-Nets in Base 32

Best Known (78−56, 78, s)-Nets in Base 32

(78−56, 78, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 78, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 78, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(78−56, 78, 177)-Net in Base 32 — Constructive

(22, 78, 177)-net in base 32, using

12 times m-reduction [i] based on (22, 90, 177)-net in base 32, using
- base change [i] based on digital (7, 75, 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]

(78−56, 78, 185)-Net over F₃₂ — Digital

Digital (22, 78, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 78, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(78−56, 78, 209)-Net in Base 32

(22, 78, 209)-net in base 32, using

base change [i] based on digital (9, 65, 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]

(78−56, 78, 5668)-Net in Base 32 — Upper bound on s

There is no (22, 78, 5669)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2529 337228 509733 869732 520335 668214 615915 362258 095063 902889 037622 812586 644049 937947 055137 727755 273817 093762 770452 657844 > 32⁷⁸ [i]