MinT - Best Known (16, 16+83, s)-Nets in Base 32

Best Known (16, 16+83, s)-Nets in Base 32

(16, 16+83, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 99, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 99, 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+83, 158)-Net over F₃₂ — Digital

Digital (16, 99, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 99, 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+83, 2040)-Net in Base 32 — Upper bound on s

There is no (16, 99, 2041)-net in base 32, because

1 times m-reduction [i] would yield (16, 98, 2041)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3233 064525 616275 718604 664938 089510 343740 714405 073618 674002 381593 049529 027927 881474 218817 227310 421897 207766 632412 237073 891705 822953 677578 028732 601328 > 32⁹⁸ [i]