MinT - Best Known (25, 25+77, s)-Nets in Base 32

Best Known (25, 25+77, s)-Nets in Base 32

(25, 25+77, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 102, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 102, 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+77, 177)-Net in Base 32 — Constructive

(25, 102, 177)-net in base 32, using

6 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+77, 225)-Net over F₃₂ — Digital

Digital (25, 102, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 102, 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+77, 4832)-Net in Base 32 — Upper bound on s

There is no (25, 102, 4833)-net in base 32, because

1 times m-reduction [i] would yield (25, 101, 4833)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 104 863419 203890 820018 592929 565936 909523 565883 979941 646770 094729 402671 390195 041077 446188 874495 335536 893460 208094 278349 308029 618874 253343 590993 923171 417760 > 32¹⁰¹ [i]