MinT - Best Known (66−25, 66, s)-Nets in Base 32

Best Known (66−25, 66, s)-Nets in Base 32

(66−25, 66, 294)-Net over F₃₂ — Constructive and digital

Digital (41, 66, 294)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 15, 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, 19, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
3. digital (7, 32, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(66−25, 66, 518)-Net in Base 32 — Constructive

(41, 66, 518)-net in base 32, using

base change [i] based on (30, 55, 518)-net in base 64, using
- (u,Â u+v)-construction [i] based on
  1. (7, 19, 259)-net in base 64, using
    - 1 times m-reduction [i] based on (7, 20, 259)-net in base 64, using
      - base change [i] based on digital (2, 15, 259)-net over F₂₅₆, using
        net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. (11, 36, 259)-net in base 64, using
    - base change [i] based on digital (2, 27, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(66−25, 66, 4369)-Net over F₃₂ — Digital

Digital (41, 66, 4369)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(66−25, 66, large)-Net in Base 32 — Upper bound on s

There is no (41, 66, large)-net in base 32, because

23 times m-reduction [i] would yield (41, 43, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]