MinT - Best Known (84−71, 84, s)-Nets in Base 32

Best Known (84−71, 84, s)-Nets in Base 32

(84−71, 84, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 84, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 84, 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]

(84−71, 84, 129)-Net over F₃₂ — Digital

Digital (13, 84, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 84, 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]

(84−71, 84, 1646)-Net in Base 32 — Upper bound on s

There is no (13, 84, 1647)-net in base 32, because

1 times m-reduction [i] would yield (13, 83, 1647)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 85845 082219 802499 211694 311695 544237 388162 590127 200372 825531 291499 348866 096121 312677 295019 136626 454779 320349 902991 536839 019132 > 32⁸³ [i]