MinT - Best Known (26, 26+17, s)-Nets in Base 32

Best Known (26, 26+17, s)-Nets in Base 32

(26, 26+17, 264)-Net over F₃₂ — Constructive and digital

Digital (26, 43, 264)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 2, 33)-net over F₃₂, using
  - kÂ =Â 2 construction [i]
2. digital (0, 2, 33)-net over F₃₂ (see above)
3. digital (0, 2, 33)-net over F₃₂ (see above)
4. digital (0, 3, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
      - the rational function field F₃₂(x) [i]
    - Niederreiter sequence [i]
5. digital (0, 4, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
6. digital (0, 5, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
7. digital (0, 8, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
8. digital (0, 17, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)

(26, 26+17, 515)-Net in Base 32 — Constructive

(26, 43, 515)-net in base 32, using

32¹ times duplication [i] based on (25, 42, 515)-net in base 32, using
- base change [i] based on (18, 35, 515)-net in base 64, using
  - (u,Â u+v)-construction [i] based on
    1. (3, 11, 257)-net in base 64, using
      - 1 times m-reduction [i] based on (3, 12, 257)-net in base 64, using
        base change [i] based on digital (0, 9, 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. (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]

(26, 26+17, 2442)-Net over F₃₂ — Digital

Digital (26, 43, 2442)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(26, 26+17, large)-Net in Base 32 — Upper bound on s

There is no (26, 43, large)-net in base 32, because

15 times m-reduction [i] would yield (26, 28, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]