MinT - Best Known (80−63, 80, s)-Nets in Base 32

Best Known (80−63, 80, s)-Nets in Base 32

(80−63, 80, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 80, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 80, 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]

(80−63, 80, 158)-Net over F₃₂ — Digital

Digital (17, 80, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 80, 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]

(80−63, 80, 2727)-Net in Base 32 — Upper bound on s

There is no (17, 80, 2728)-net in base 32, because

1 times m-reduction [i] would yield (17, 79, 2728)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 80723 308384 400983 782662 587137 764635 392291 741198 310909 377272 614120 463796 034695 339674 380945 450365 010578 802562 409022 152748 > 32⁷⁹ [i]