MinT - Best Known (31, 31+71, s)-Nets in Base 32

Best Known (31, 31+71, s)-Nets in Base 32

(31, 31+71, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 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]

(31, 31+71, 177)-Net in Base 32 — Constructive

(31, 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]

(31, 31+71, 273)-Net over F₃₂ — Digital

Digital (31, 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]

(31, 31+71, 9875)-Net in Base 32 — Upper bound on s

There is no (31, 102, 9876)-net in base 32, because

1 times m-reduction [i] would yield (31, 101, 9876)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 105 106745 307005 642778 393607 390794 021339 652424 422022 335822 680618 850865 103198 471725 634983 757415 421517 612590 471867 548812 456524 331960 275965 867913 585285 442748 > 32¹⁰¹ [i]