MinT - Best Known (105−73, 105, s)-Nets in Base 32

Best Known (105−73, 105, s)-Nets in Base 32

(105−73, 105, 120)-Net over F₃₂ — Constructive and digital

Digital (32, 105, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 105, 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]

(105−73, 105, 177)-Net in Base 32 — Constructive

(32, 105, 177)-net in base 32, using

t-expansion [i] based on (25, 105, 177)-net in base 32, using
- 3 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]

(105−73, 105, 273)-Net over F₃₂ — Digital

Digital (32, 105, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 105, 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]

(105−73, 105, 10251)-Net in Base 32 — Upper bound on s

There is no (32, 105, 10252)-net in base 32, because

1 times m-reduction [i] would yield (32, 104, 10252)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 435716 990639 572978 101294 423661 147302 049595 946034 340386 389436 321693 576035 832673 117364 444877 637093 437871 605409 261040 471473 396216 158709 009055 588152 407316 237184 > 32¹⁰⁴ [i]