MinT - Best Known (21, 21+89, s)-Nets in Base 32

Best Known (21, 21+89, s)-Nets in Base 32

(21, 21+89, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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]

(21, 21+89, 185)-Net over F₃₂ — Digital

Digital (21, 110, 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]

(21, 21+89, 2957)-Net in Base 32 — Upper bound on s

There is no (21, 110, 2958)-net in base 32, because

1 times m-reduction [i] would yield (21, 109, 2958)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 116 542511 103757 894810 729105 534580 402930 173967 011045 302202 646000 917748 577828 161969 513803 402721 699936 911552 894398 558093 860016 875608 369297 536455 498054 421333 286075 902180 > 32¹⁰⁹ [i]