MinT - Best Known (28, 28+81, s)-Nets in Base 32

Best Known (28, 28+81, s)-Nets in Base 32

(28, 28+81, 120)-Net over F₃₂ — Constructive and digital

Digital (28, 109, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 109, 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]

(28, 28+81, 177)-Net in Base 32 — Constructive

(28, 109, 177)-net in base 32, using

32¹ times duplication [i] based on (27, 108, 177)-net in base 32, using
- t-expansion [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]

(28, 28+81, 257)-Net over F₃₂ — Digital

Digital (28, 109, 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]

(28, 28+81, 5872)-Net in Base 32 — Upper bound on s

There is no (28, 109, 5873)-net in base 32, because

1 times m-reduction [i] would yield (28, 108, 5873)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 618792 319822 220562 151238 953088 804707 240497 181977 906422 922525 512536 224127 532575 774211 653346 427712 628375 821387 476012 742840 915328 702378 180779 534617 544804 061157 758286 > 32¹⁰⁸ [i]