MinT - Best Known (42, 95, s)-Nets in Base 32

Best Known (42, 95, s)-Nets in Base 32

(42, 95, 202)-Net over F₃₂ — Constructive and digital

Digital (42, 95, 202)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 33, 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 (9, 62, 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]

(42, 95, 288)-Net in Base 32 — Constructive

(42, 95, 288)-net in base 32, using

t-expansion [i] based on (40, 95, 288)-net in base 32, using
- 13 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
  - base change [i] based on (22, 90, 288)-net in base 64, using
    - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
      - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
        net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(42, 95, 361)-Net over F₃₂ — Digital

Digital (42, 95, 361)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 95, 425)-Net in Base 32

(42, 95, 425)-net in base 32, using

1 times m-reduction [i] based on (42, 96, 425)-net in base 32, using
- base change [i] based on digital (26, 80, 425)-net over F₆₄, using
  - net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
      - a curve from the manYPoints database [i]

(42, 95, 94094)-Net in Base 32 — Upper bound on s

There is no (42, 95, 94095)-net in base 32, because

1 times m-reduction [i] would yield (42, 94, 94095)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3048 707384 710926 293666 727699 393158 065997 420990 684821 595264 392516 799727 772400 781653 497017 376675 158314 227581 705194 987773 361090 129788 212194 189080 > 32⁹⁴ [i]