MinT - Best Known (102−70, 102, s)-Nets in Base 32

Best Known (102−70, 102, s)-Nets in Base 32

(102−70, 102, 120)-Net over F₃₂ — Constructive and digital

Digital (32, 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]

(102−70, 102, 177)-Net in Base 32 — Constructive

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

t-expansion [i] based on (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]

(102−70, 102, 273)-Net over F₃₂ — Digital

Digital (32, 102, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 102, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(102−70, 102, 10904)-Net in Base 32 — Upper bound on s

There is no (32, 102, 10905)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3354 013865 832055 102877 475043 491366 492271 435659 905343 219873 058008 108556 415510 335579 166139 750549 125148 649150 285067 146746 583903 931676 469150 522633 589562 498912 > 32¹⁰² [i]