MinT - Best Known (30, 30+35, s)-Nets in Base 32

Best Known (30, 30+35, s)-Nets in Base 32

(30, 30+35, 174)-Net over F₃₂ — Constructive and digital

Digital (30, 65, 174)-net over F₃₂, using

1 times m-reduction [i] based on digital (30, 66, 174)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 23, 76)-net over F₃₂, using
    - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
        a function field by SÃ©mirat [i]
  2. digital (7, 43, 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]

(30, 30+35, 288)-Net in Base 32 — Constructive

(30, 65, 288)-net in base 32, using

7 times m-reduction [i] based on (30, 72, 288)-net in base 32, using
- base change [i] based on (18, 60, 288)-net in base 64, using
  - 3 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
    - base change [i] based on digital (9, 54, 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]

(30, 30+35, 339)-Net over F₃₂ — Digital

Digital (30, 65, 339)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 30+35, 107397)-Net in Base 32 — Upper bound on s

There is no (30, 65, 107398)-net in base 32, because

1 times m-reduction [i] would yield (30, 64, 107398)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 136009 575055 920297 226112 701643 030358 297108 243486 599575 109968 689061 464597 589934 587665 067464 531128 > 32⁶⁴ [i]