MinT - Best Known (105−72, 105, s)-Nets in Base 32

Best Known (105−72, 105, s)-Nets in Base 32

(105−72, 105, 120)-Net over F₃₂ — Constructive and digital

Digital (33, 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]

(105−72, 105, 192)-Net in Base 32 — Constructive

(33, 105, 192)-net in base 32, using

base change [i] based on digital (3, 75, 192)-net over F₁₂₈, using
- net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
    - a function field by SÃ©mirat [i]

(105−72, 105, 273)-Net over F₃₂ — Digital

Digital (33, 105, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 105, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(105−72, 105, 11289)-Net in Base 32 — Upper bound on s

There is no (33, 105, 11290)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 109 971398 101058 511679 342800 169461 260167 043807 868978 620305 646213 844663 860026 573371 419092 493558 510288 595743 799828 152790 799942 433196 893625 619241 028064 486197 353664 > 32¹⁰⁵ [i]