MinT - Best Known (48, 48+31, s)-Nets in Base 32

Best Known (48, 48+31, s)-Nets in Base 32

(48, 48+31, 300)-Net over F₃₂ — Constructive and digital

Digital (48, 79, 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, 22, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
3. digital (9, 40, 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]

(48, 48+31, 517)-Net in Base 32 — Constructive

(48, 79, 517)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (9, 24, 257)-net in base 32, using
  - base change [i] based on digital (0, 15, 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. (24, 55, 260)-net in base 32, using
  - 1 times m-reduction [i] based on (24, 56, 260)-net in base 32, using
    - base change [i] based on digital (3, 35, 260)-net over F₂₅₆, using
      - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(48, 48+31, 3588)-Net over F₃₂ — Digital

Digital (48, 79, 3588)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+31, large)-Net in Base 32 — Upper bound on s

There is no (48, 79, large)-net in base 32, because

29 times m-reduction [i] would yield (48, 50, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]