MinT - Best Known (98−73, 98, s)-Nets in Base 32

Best Known (98−73, 98, s)-Nets in Base 32

(98−73, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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]

(98−73, 98, 177)-Net in Base 32 — Constructive

(25, 98, 177)-net in base 32, using

10 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]

(98−73, 98, 225)-Net over F₃₂ — Digital

Digital (25, 98, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 98, 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]

(98−73, 98, 5216)-Net in Base 32 — Upper bound on s

There is no (25, 98, 5217)-net in base 32, because

1 times m-reduction [i] would yield (25, 97, 5217)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 100 327194 014446 169773 927374 505780 189237 679518 321279 271608 707485 593094 102962 608413 503632 765944 704693 190813 608551 069821 156547 432651 032370 189340 962960 > 32⁹⁷ [i]