MinT - Best Known (85−73, 85, s)-Nets in Base 32

Best Known (85−73, 85, s)-Nets in Base 32

(85−73, 85, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 85, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 85, 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]

(85−73, 85, 129)-Net over F₃₂ — Digital

Digital (12, 85, 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]

(85−73, 85, 1478)-Net in Base 32 — Upper bound on s

There is no (12, 85, 1479)-net in base 32, because

1 times m-reduction [i] would yield (12, 84, 1479)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 709283 184300 558604 199188 204119 657178 983151 464462 706680 144785 514493 481746 171595 359607 794490 323013 102765 110410 147554 778368 022390 > 32⁸⁴ [i]