MinT - Best Known (89−76, 89, s)-Nets in Base 32

Best Known (89−76, 89, s)-Nets in Base 32

(89−76, 89, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 89, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 89, 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]

(89−76, 89, 129)-Net over F₃₂ — Digital

Digital (13, 89, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 89, 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]

(89−76, 89, 1604)-Net in Base 32 — Upper bound on s

There is no (13, 89, 1605)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 91 695021 679104 489316 344062 517694 437266 636611 488649 975307 327877 577829 856462 368774 132364 958122 218580 786062 848894 190649 426762 353538 674784 > 32⁸⁹ [i]