MinT - Best Known (87−44, 87, s)-Nets in Base 32

Best Known (87−44, 87, s)-Nets in Base 32

(87−44, 87, 224)-Net over F₃₂ — Constructive and digital

Digital (43, 87, 224)-net over F₃₂, using

2 times m-reduction [i] based on digital (43, 89, 224)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 32, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]
  2. digital (11, 57, 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]

(87−44, 87, 513)-Net in Base 32 — Constructive

(43, 87, 513)-net in base 32, using

3 times m-reduction [i] based on (43, 90, 513)-net in base 32, using
- base change [i] based on digital (28, 75, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(87−44, 87, 625)-Net over F₃₂ — Digital

Digital (43, 87, 625)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−44, 87, 261611)-Net in Base 32 — Upper bound on s

There is no (43, 87, 261612)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 88729 614633 690859 355904 047139 316689 003337 844701 552887 143651 053158 959765 683733 310543 782266 481161 847270 352316 535451 800371 989129 797692 > 32⁸⁷ [i]