MinT - Best Known (69−55, 69, s)-Nets in Base 32

Best Known (69−55, 69, s)-Nets in Base 32

(69−55, 69, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 69, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 69, 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]

(69−55, 69, 146)-Net over F₃₂ — Digital

Digital (14, 69, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(69−55, 69, 2162)-Net in Base 32 — Upper bound on s

There is no (14, 69, 2163)-net in base 32, because

1 times m-reduction [i] would yield (14, 68, 2163)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 244717 211727 776651 054001 690496 473204 300072 639586 056607 894233 575965 533866 263470 208992 902228 439399 686624 > 32⁶⁸ [i]