MinT - Best Known (12, 12+67, s)-Nets in Base 32

Best Known (12, 12+67, s)-Nets in Base 32

(12, 12+67, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 79, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 79, 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+67, 129)-Net over F₃₂ — Digital

Digital (12, 79, 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+67, 1516)-Net in Base 32 — Upper bound on s

There is no (12, 79, 1517)-net in base 32, because

1 times m-reduction [i] would yield (12, 78, 1517)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2562 756933 245142 237886 976606 349869 118259 664777 430641 367307 281647 928267 984881 102051 092967 656177 713560 433886 298394 501740 > 32⁷⁸ [i]