MinT - Best Known (74−29, 74, s)-Nets in Base 32

Best Known (74−29, 74, s)-Nets in Base 32

(74−29, 74, 294)-Net over F₃₂ — Constructive and digital

Digital (45, 74, 294)-net over F₃₂, using

32¹ times duplication [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)

(74−29, 74, 516)-Net in Base 32 — Constructive

(45, 74, 516)-net in base 32, using

32² times duplication [i] based on (43, 72, 516)-net in base 32, using
- base change [i] based on digital (16, 45, 516)-net over F₂₅₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (1, 15, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
    2. digital (1, 30, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(74−29, 74, 3478)-Net over F₃₂ — Digital

Digital (45, 74, 3478)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−29, 74, large)-Net in Base 32 — Upper bound on s

There is no (45, 74, large)-net in base 32, because

27 times m-reduction [i] would yield (45, 47, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]