MinT - Best Known (71−27, 71, s)-Nets in Base 32

Best Known (71−27, 71, s)-Nets in Base 32

(71−27, 71, 294)-Net over F₃₂ — Constructive and digital

Digital (44, 71, 294)-net over F₃₂, using

2 times m-reduction [i] based on digital (44, 73, 294)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 16, 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, 21, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (7, 36, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(71−27, 71, 518)-Net in Base 32 — Constructive

(44, 71, 518)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (11, 24, 259)-net in base 32, using
  - base change [i] based on digital (2, 15, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. (20, 47, 259)-net in base 32, using
  - 1 times m-reduction [i] based on (20, 48, 259)-net in base 32, using
    - base change [i] based on digital (2, 30, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(71−27, 71, 4400)-Net over F₃₂ — Digital

Digital (44, 71, 4400)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(71−27, 71, large)-Net in Base 32 — Upper bound on s

There is no (44, 71, large)-net in base 32, because

25 times m-reduction [i] would yield (44, 46, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]