MinT - Best Known (98−69, 98, s)-Nets in Base 32

Best Known (98−69, 98, s)-Nets in Base 32

(98−69, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 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]

(98−69, 98, 177)-Net in Base 32 — Constructive

(29, 98, 177)-net in base 32, using

t-expansion [i] based on (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]

(98−69, 98, 257)-Net over F₃₂ — Digital

Digital (29, 98, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 98, 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]

(98−69, 98, 8576)-Net in Base 32 — Upper bound on s

There is no (29, 98, 8577)-net in base 32, because

1 times m-reduction [i] would yield (29, 97, 8577)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 99 950930 767900 207519 097156 906668 102187 483568 784980 311733 837067 131034 675340 824839 055408 984982 311422 641948 979072 218178 455297 775888 651909 994981 817920 > 32⁹⁷ [i]