MinT - Best Known (16, 16+71, s)-Nets in Base 32

Best Known (16, 16+71, s)-Nets in Base 32

(16, 16+71, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 87, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 87, 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]

(16, 16+71, 158)-Net over F₃₂ — Digital

Digital (16, 87, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 87, 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]

(16, 16+71, 2222)-Net in Base 32 — Upper bound on s

There is no (16, 87, 2223)-net in base 32, because

1 times m-reduction [i] would yield (16, 86, 2223)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2815 482258 422171 003112 731611 555467 888193 562715 029462 939031 725138 549258 212859 621062 703469 572005 498080 605805 950100 726918 064348 127220 > 32⁸⁶ [i]