MinT - Best Known (29, 29+71, s)-Nets in Base 32

Best Known (29, 29+71, s)-Nets in Base 32

(29, 29+71, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 100, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 100, 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]

(29, 29+71, 177)-Net in Base 32 — Constructive

(29, 100, 177)-net in base 32, using

t-expansion [i] based on (25, 100, 177)-net in base 32, using
- 8 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]

(29, 29+71, 257)-Net over F₃₂ — Digital

Digital (29, 100, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 100, 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]

(29, 29+71, 8097)-Net in Base 32 — Upper bound on s

There is no (29, 100, 8098)-net in base 32, because

1 times m-reduction [i] would yield (29, 99, 8098)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 102476 268932 671217 608529 206821 236363 559355 746242 459152 674485 748468 017185 020608 451947 458201 704173 530877 202559 516310 525964 165822 004352 192074 520082 249280 > 32⁹⁹ [i]