MinT - Best Known (49, 81, s)-Nets in Base 32

Best Known (49, 81, s)-Nets in Base 32

(49, 81, 300)-Net over F₃₂ — Constructive and digital

Digital (49, 81, 300)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 17, 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, 23, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
3. digital (9, 41, 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]

(49, 81, 516)-Net in Base 32 — Constructive

(49, 81, 516)-net in base 32, using

32¹ times duplication [i] based on (48, 80, 516)-net in base 32, using
- base change [i] based on digital (18, 50, 516)-net over F₂₅₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (1, 17, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
    2. digital (1, 33, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(49, 81, 3447)-Net over F₃₂ — Digital

Digital (49, 81, 3447)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 81, large)-Net in Base 32 — Upper bound on s

There is no (49, 81, large)-net in base 32, because

30 times m-reduction [i] would yield (49, 51, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]