MinT - Best Known (97−71, 97, s)-Nets in Base 32

Best Known (97−71, 97, s)-Nets in Base 32

(97−71, 97, 120)-Net over F₃₂ — Constructive and digital

Digital (26, 97, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 97, 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]

(97−71, 97, 177)-Net in Base 32 — Constructive

(26, 97, 177)-net in base 32, using

t-expansion [i] based on (25, 97, 177)-net in base 32, using
- 11 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]

(97−71, 97, 225)-Net over F₃₂ — Digital

Digital (26, 97, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 97, 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]

(97−71, 97, 6011)-Net in Base 32 — Upper bound on s

There is no (26, 97, 6012)-net in base 32, because

1 times m-reduction [i] would yield (26, 96, 6012)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 124843 228754 777948 593168 666217 564468 266879 499338 561234 457316 033182 208674 594768 370276 271807 991762 280950 898956 387328 968823 301384 365367 741185 904751 > 32⁹⁶ [i]