MinT - Best Known (105−83, 105, s)-Nets in Base 32

Best Known (105−83, 105, s)-Nets in Base 32

(105−83, 105, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 105, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 105, 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]

(105−83, 105, 185)-Net over F₃₂ — Digital

Digital (22, 105, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 105, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(105−83, 105, 3402)-Net in Base 32 — Upper bound on s

There is no (22, 105, 3403)-net in base 32, because

1 times m-reduction [i] would yield (22, 104, 3403)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 457915 567057 948157 392635 692498 841219 926786 964333 317228 426227 313077 520802 511176 459160 952135 224904 598360 215441 803958 708065 822890 213154 074870 302616 005005 410116 > 32¹⁰⁴ [i]