MinT - Best Known (15, 15+38, s)-Nets in Base 32

Best Known (15, 15+38, s)-Nets in Base 32

(15, 15+38, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 53, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 53, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(15, 15+38, 128)-Net in Base 32 — Constructive

(15, 53, 128)-net in base 32, using

7 times m-reduction [i] based on (15, 60, 128)-net in base 32, using
- base change [i] based on digital (5, 50, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(15, 15+38, 158)-Net over F₃₂ — Digital

Digital (15, 53, 158)-net over F₃₂, using

net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
  - an algebraic function field by Beelen and Pellikaan [i]

(15, 15+38, 161)-Net in Base 32

(15, 53, 161)-net in base 32, using

1 times m-reduction [i] based on (15, 54, 161)-net in base 32, using
- base change [i] based on digital (6, 45, 161)-net over F₆₄, using
  - net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

(15, 15+38, 4030)-Net in Base 32 — Upper bound on s

There is no (15, 53, 4031)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 59 328693 955567 892804 347510 676310 718732 014834 339146 186435 505292 735318 790950 576740 > 32⁵³ [i]