MinT - Best Known (80−67, 80, s)-Nets in Base 32

Best Known (80−67, 80, s)-Nets in Base 32

(80−67, 80, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 80, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 80, 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]

(80−67, 80, 129)-Net over F₃₂ — Digital

Digital (13, 80, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 80, 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]

(80−67, 80, 1686)-Net in Base 32 — Upper bound on s

There is no (13, 80, 1687)-net in base 32, because

1 times m-reduction [i] would yield (13, 79, 1687)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 82220 352851 473982 292212 719574 304427 202127 845166 202578 559095 153488 447403 843092 737021 490129 422838 855020 684222 643478 010280 > 32⁷⁹ [i]