MinT - Best Known (16, 16+85, s)-Nets in Base 32

Best Known (16, 16+85, s)-Nets in Base 32

(16, 16+85, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 101, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 101, 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+85, 158)-Net over F₃₂ — Digital

Digital (16, 101, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 101, 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+85, 2020)-Net in Base 32 — Upper bound on s

There is no (16, 101, 2021)-net in base 32, because

1 times m-reduction [i] would yield (16, 100, 2021)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 304020 323969 629854 016396 358298 614910 750277 262360 954834 436537 089699 460788 473151 964803 909267 277724 001985 395574 971336 328554 431704 778661 865700 289560 324688 > 32¹⁰⁰ [i]