MinT - Best Known (96−40, 96, s)-Nets in Base 32

Best Known (96−40, 96, s)-Nets in Base 32

(96−40, 96, 300)-Net over F₃₂ — Constructive and digital

Digital (56, 96, 300)-net over F₃₂, using

1 times m-reduction [i] based on digital (56, 97, 300)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 20, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]
  2. digital (7, 27, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (9, 50, 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]

(96−40, 96, 514)-Net in Base 32 — Constructive

(56, 96, 514)-net in base 32, using

base change [i] based on digital (20, 60, 514)-net over F₂₅₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 20, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]
  2. digital (0, 40, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(96−40, 96, 2537)-Net over F₃₂ — Digital

Digital (56, 96, 2537)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−40, 96, 4494314)-Net in Base 32 — Upper bound on s

There is no (56, 96, 4494315)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 121756 546127 842695 274950 576578 203304 268097 063104 840359 517290 940846 720514 336057 554559 142187 227039 788998 982163 141438 547691 250153 517807 253905 490564 > 32⁹⁶ [i]