MinT - Best Known (107−91, 107, s)-Nets in Base 32

Best Known (107−91, 107, s)-Nets in Base 32

(107−91, 107, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 107, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 107, 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]

(107−91, 107, 158)-Net over F₃₂ — Digital

Digital (16, 107, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 107, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(107−91, 107, 1973)-Net in Base 32 — Upper bound on s

There is no (16, 107, 1974)-net in base 32, because

1 times m-reduction [i] would yield (16, 106, 1974)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3583 628922 786075 017933 629558 302215 220643 202468 302193 630035 464894 281427 122035 913976 965115 920221 216796 427308 099824 321927 089218 047716 614982 079574 481563 935052 583810 > 32¹⁰⁶ [i]