MinT - Best Known (96−49, 96, s)-Nets in Base 32

Best Known (96−49, 96, s)-Nets in Base 32

(96−49, 96, 240)-Net over F₃₂ — Constructive and digital

Digital (47, 96, 240)-net over F₃₂, using

1 times m-reduction [i] based on digital (47, 97, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 36, 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]
  2. digital (11, 61, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(96−49, 96, 513)-Net in Base 32 — Constructive

(47, 96, 513)-net in base 32, using

t-expansion [i] based on (46, 96, 513)-net in base 32, using
- 12 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
  - base change [i] based on digital (28, 90, 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]

(96−49, 96, 632)-Net over F₃₂ — Digital

Digital (47, 96, 632)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−49, 96, 286990)-Net in Base 32 — Upper bound on s

There is no (47, 96, 286991)-net in base 32, because

1 times m-reduction [i] would yield (47, 95, 286991)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 97557 218288 204773 515607 313441 169063 338647 404784 131285 667359 347833 986516 759852 741862 487231 641118 702832 825051 685855 003542 083259 180811 755936 656752 > 32⁹⁵ [i]