MinT - Best Known (89−61, 89, s)-Nets in Base 32

Best Known (89−61, 89, s)-Nets in Base 32

(89−61, 89, 120)-Net over F₃₂ — Constructive and digital

Digital (28, 89, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 89, 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]

(89−61, 89, 177)-Net in Base 32 — Constructive

(28, 89, 177)-net in base 32, using

t-expansion [i] based on (25, 89, 177)-net in base 32, using
- 19 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]

(89−61, 89, 257)-Net over F₃₂ — Digital

Digital (28, 89, 257)-net over F₃₂, using

net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
  - a curve from the manYPoints database [i]

(89−61, 89, 10089)-Net in Base 32 — Upper bound on s

There is no (28, 89, 10090)-net in base 32, because

1 times m-reduction [i] would yield (28, 88, 10090)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 843653 767948 573309 462706 294526 941235 059823 706838 091854 867620 791620 373300 307546 663712 436995 130995 072842 745068 712890 246795 884731 882800 > 32⁸⁸ [i]