MinT - Best Known (97−69, 97, s)-Nets in Base 32

Best Known (97−69, 97, s)-Nets in Base 32

(97−69, 97, 120)-Net over F₃₂ — Constructive and digital

Digital (28, 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]

(97−69, 97, 177)-Net in Base 32 — Constructive

(28, 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]

(97−69, 97, 257)-Net over F₃₂ — Digital

Digital (28, 97, 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]

(97−69, 97, 7743)-Net in Base 32 — Upper bound on s

There is no (28, 97, 7744)-net in base 32, because

1 times m-reduction [i] would yield (28, 96, 7744)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 122146 150941 428590 100511 437304 853799 230441 691604 064747 415706 565627 929331 873490 621481 451227 444045 237958 864812 855467 355313 819210 279941 348394 702515 > 32⁹⁶ [i]