MinT - Best Known (91−68, 91, s)-Nets in Base 32

Best Known (91−68, 91, s)-Nets in Base 32

(91−68, 91, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 91, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 91, 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]

(91−68, 91, 177)-Net in Base 32 — Constructive

(23, 91, 177)-net in base 32, using

5 times m-reduction [i] based on (23, 96, 177)-net in base 32, using
- base change [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]

(91−68, 91, 185)-Net over F₃₂ — Digital

Digital (23, 91, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 91, 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]

(91−68, 91, 4644)-Net in Base 32 — Upper bound on s

There is no (23, 91, 4645)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93204 062720 886564 299466 178730 581430 929219 554089 232415 540830 343612 085909 871902 503178 724743 856109 229825 416440 263425 723113 383933 488326 007830 > 32⁹¹ [i]