MinT - Best Known (92−38, 92, s)-Nets in Base 32

Best Known (92−38, 92, s)-Nets in Base 32

(92−38, 92, 300)-Net over F₃₂ — Constructive and digital

Digital (54, 92, 300)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 19, 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, 26, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
3. digital (9, 47, 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]

(92−38, 92, 513)-Net in Base 32 — Constructive

(54, 92, 513)-net in base 32, using

t-expansion [i] based on (46, 92, 513)-net in base 32, using
- 16 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
  - base change [i] based on digital (28, 90, 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]

(92−38, 92, 2631)-Net over F₃₂ — Digital

Digital (54, 92, 2631)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−38, 92, 4965324)-Net in Base 32 — Upper bound on s

There is no (54, 92, 4965325)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 977141 368850 313445 803907 303071 530452 060210 757738 200124 688534 986093 862254 086691 347889 836704 653772 298360 625383 247127 622244 128750 621516 293936 > 32⁹² [i]