MinT - Best Known (90−46, 90, s)-Nets in Base 32

Best Known (90−46, 90, s)-Nets in Base 32

(90−46, 90, 224)-Net over F₃₂ — Constructive and digital

Digital (44, 90, 224)-net over F₃₂, using

2 times m-reduction [i] based on digital (44, 92, 224)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 33, 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, 59, 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]

(90−46, 90, 513)-Net in Base 32 — Constructive

(44, 90, 513)-net in base 32, using

6 times m-reduction [i] based on (44, 96, 513)-net in base 32, using
- base change [i] based on digital (28, 80, 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]

(90−46, 90, 597)-Net over F₃₂ — Digital

Digital (44, 90, 597)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−46, 90, 235933)-Net in Base 32 — Upper bound on s

There is no (44, 90, 235934)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2907 393660 784226 810505 696455 037280 226364 406004 845202 633993 571833 964862 819854 029127 131312 879127 345871 196346 963383 770713 139058 405267 769044 > 32⁹⁰ [i]