MinT - Best Known (104−83, 104, s)-Nets in Base 32

Best Known (104−83, 104, s)-Nets in Base 32

(104−83, 104, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 104, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 104, 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]

(104−83, 104, 185)-Net over F₃₂ — Digital

Digital (21, 104, 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]

(104−83, 104, 3124)-Net in Base 32 — Upper bound on s

There is no (21, 104, 3125)-net in base 32, because

1 times m-reduction [i] would yield (21, 103, 3125)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107438 229821 579381 664245 042005 893803 202731 286910 421024 402795 481761 110377 020366 712506 883009 309740 627762 425520 536811 890452 593940 076885 644019 824888 553941 296376 > 32¹⁰³ [i]