MinT - Best Known (67−55, 67, s)-Nets in Base 32

Best Known (67−55, 67, s)-Nets in Base 32

(67−55, 67, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 67, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 67, 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]

(67−55, 67, 129)-Net over F₃₂ — Digital

Digital (12, 67, 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]

(67−55, 67, 1669)-Net in Base 32 — Upper bound on s

There is no (12, 67, 1670)-net in base 32, because

1 times m-reduction [i] would yield (12, 66, 1670)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2187 495959 092244 805173 963558 592832 012200 376655 425172 984793 709999 266396 408150 275383 502962 729830 366048 > 32⁶⁶ [i]