MinT - Best Known (24−17, 24, s)-Nets in Base 32

Best Known (24−17, 24, s)-Nets in Base 32

(24−17, 24, 98)-Net over F₃₂ — Constructive and digital

Digital (7, 24, 98)-net over F₃₂, using

net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
  - a function field by SÃ©mirat [i]

(24−17, 24, 129)-Net in Base 32 — Constructive

(7, 24, 129)-net in base 32, using

base change [i] based on (3, 20, 129)-net in base 64, using
- 1 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
  - base change [i] based on digital (0, 18, 129)-net over F₁₂₈, using
    - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
      - Niederreiter sequence [i]

(24−17, 24, 2576)-Net in Base 32 — Upper bound on s

There is no (7, 24, 2577)-net in base 32, because

1 times m-reduction [i] would yield (7, 23, 2577)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 41624 546696 005670 884289 516710 806790 > 32²³ [i]