MinT - Best Known (103−81, 103, s)-Nets in Base 32

Best Known (103−81, 103, s)-Nets in Base 32

(103−81, 103, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 103, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 103, 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]

(103−81, 103, 185)-Net over F₃₂ — Digital

Digital (22, 103, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 103, 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]

(103−81, 103, 3483)-Net in Base 32 — Upper bound on s

There is no (22, 103, 3484)-net in base 32, because

1 times m-reduction [i] would yield (22, 102, 3484)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3381 999268 812789 581429 123967 180121 033708 872938 678919 807775 016729 010347 401541 614238 885842 937764 528279 379603 146812 659257 311581 872900 511524 119613 295000 322340 > 32¹⁰² [i]