MinT - Best Known (78−30, 78, s)-Nets in Base 32

Best Known (78−30, 78, s)-Nets in Base 32

(78−30, 78, 300)-Net over F₃₂ — Constructive and digital

Digital (48, 78, 300)-net over F₃₂, using

1 times m-reduction [i] based on 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]

(78−30, 78, 517)-Net in Base 32 — Constructive

(48, 78, 517)-net in base 32, using

base change [i] based on (35, 65, 517)-net in base 64, using
- 1 times m-reduction [i] based on (35, 66, 517)-net in base 64, using
  - (u,Â u+v)-construction [i] based on
    1. (7, 22, 258)-net in base 64, using
      - 2 times m-reduction [i] based on (7, 24, 258)-net in base 64, using
        base change [i] based on digital (1, 18, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
    2. (13, 44, 259)-net in base 64, using
      - base change [i] based on digital (2, 33, 259)-net over F₂₅₆, using
        net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(78−30, 78, 4223)-Net over F₃₂ — Digital

Digital (48, 78, 4223)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−30, 78, large)-Net in Base 32 — Upper bound on s

There is no (48, 78, large)-net in base 32, because

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