MinT - Best Known (64, 102, s)-Nets in Base 32

Best Known (64, 102, s)-Nets in Base 32

(64, 102, 360)-Net over F₃₂ — Constructive and digital

Digital (64, 102, 360)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (11, 23, 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]
2. digital (11, 30, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)
3. digital (11, 49, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(64, 102, 578)-Net in Base 32 — Constructive

(64, 102, 578)-net in base 32, using

base change [i] based on digital (47, 85, 578)-net over F₆₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 19, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
  2. digital (28, 66, 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]

(64, 102, 6685)-Net over F₃₂ — Digital

Digital (64, 102, 6685)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 102, large)-Net in Base 32 — Upper bound on s

There is no (64, 102, large)-net in base 32, because

36 times m-reduction [i] would yield (64, 66, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]