MinT - Best Known (66, 66+43, s)-Nets in Base 32

Best Known (66, 66+43, s)-Nets in Base 32

(66, 66+43, 344)-Net over F₃₂ — Constructive and digital

Digital (66, 109, 344)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (9, 23, 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]
2. digital (11, 32, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [i]
3. digital (11, 54, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(66, 66+43, 557)-Net in Base 32 — Constructive

(66, 109, 557)-net in base 32, using

1 times m-reduction [i] based on (66, 110, 557)-net in base 32, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 23, 44)-net over F₃₂, using
    - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
  2. (43, 87, 513)-net in base 32, using
    - 3 times m-reduction [i] based on (43, 90, 513)-net in base 32, using
      - base change [i] based on digital (28, 75, 513)-net over F₆₄, using
        net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(66, 66+43, 4313)-Net over F₃₂ — Digital

Digital (66, 109, 4313)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+43, large)-Net in Base 32 — Upper bound on s

There is no (66, 109, large)-net in base 32, because

41 times m-reduction [i] would yield (66, 68, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]