MinT - Best Known (25, 25+56, s)-Nets in Base 32

Best Known (25, 25+56, s)-Nets in Base 32

(25, 25+56, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 81, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 81, 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]

(25, 25+56, 177)-Net in Base 32 — Constructive

(25, 81, 177)-net in base 32, using

27 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 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]

(25, 25+56, 225)-Net over F₃₂ — Digital

Digital (25, 81, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 81, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(25, 25+56, 8223)-Net in Base 32 — Upper bound on s

There is no (25, 81, 8224)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 82 714900 961863 321153 202629 611053 962770 536111 916923 456648 097435 752933 781521 371901 665239 853463 955523 929793 618461 814681 545615 > 32⁸¹ [i]