MinT - Best Known (12, 12+81, s)-Nets in Base 32

Best Known (12, 12+81, s)-Nets in Base 32

(12, 12+81, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 93, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 93, 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]

(12, 12+81, 129)-Net over F₃₂ — Digital

Digital (12, 93, 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]

(12, 12+81, 1452)-Net in Base 32 — Upper bound on s

There is no (12, 93, 1453)-net in base 32, because

1 times m-reduction [i] would yield (12, 92, 1453)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 016559 862922 288540 155069 277577 134881 655076 416169 525163 102465 140865 520101 880575 476952 710937 873746 886284 772314 482858 008479 219574 266628 081075 > 32⁹² [i]