MinT - Best Known (27, 27+83, s)-Nets in Base 32

Best Known (27, 27+83, s)-Nets in Base 32

(27, 27+83, 120)-Net over F₃₂ — Constructive and digital

Digital (27, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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]

(27, 27+83, 177)-Net in Base 32 — Constructive

(27, 110, 177)-net in base 32, using

32² times duplication [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]

(27, 27+83, 225)-Net over F₃₂ — Digital

Digital (27, 110, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 110, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(27, 27+83, 5203)-Net in Base 32 — Upper bound on s

There is no (27, 110, 5204)-net in base 32, because

1 times m-reduction [i] would yield (27, 109, 5204)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 115 870925 162156 276310 605531 473088 435081 263345 748109 154391 278171 915818 722624 506920 994192 338058 293129 512651 923221 767356 160793 189970 534286 682595 629049 018942 933576 838900 > 32¹⁰⁹ [i]