MinT - Best Known (64−51, 64, s)-Nets in Base 32

Best Known (64−51, 64, s)-Nets in Base 32

(64−51, 64, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 64, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 64, 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]

(64−51, 64, 129)-Net over F₃₂ — Digital

Digital (13, 64, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 64, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(64−51, 64, 2025)-Net in Base 32 — Upper bound on s

There is no (13, 64, 2026)-net in base 32, because

1 times m-reduction [i] would yield (13, 63, 2026)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 67251 619181 675441 713895 732088 806612 758764 422198 236183 375962 972013 062274 277965 112781 020069 515538 > 32⁶³ [i]