MinT - Best Known (54, 54+34, s)-Nets in Base 32

Best Known (54, 54+34, s)-Nets in Base 32

(54, 54+34, 316)-Net over F₃₂ — Constructive and digital

Digital (54, 88, 316)-net over F₃₂, using

t-expansion [i] based on digital (53, 88, 316)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 18, 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, 24, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (11, 46, 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]

(54, 54+34, 518)-Net in Base 32 — Constructive

(54, 88, 518)-net in base 32, using

base change [i] based on digital (21, 55, 518)-net over F₂₅₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (2, 19, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
  2. digital (2, 36, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(54, 54+34, 4399)-Net over F₃₂ — Digital

Digital (54, 88, 4399)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+34, large)-Net in Base 32 — Upper bound on s

There is no (54, 88, large)-net in base 32, because

32 times m-reduction [i] would yield (54, 56, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]