MinT - Best Known (15, 15+87, s)-Nets in Base 32

Best Known (15, 15+87, s)-Nets in Base 32

(15, 15+87, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 102, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 102, 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]

(15, 15+87, 158)-Net over F₃₂ — Digital

Digital (15, 102, 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]

(15, 15+87, 1846)-Net in Base 32 — Upper bound on s

There is no (15, 102, 1847)-net in base 32, because

1 times m-reduction [i] would yield (15, 101, 1847)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107 127893 477632 675870 941906 709469 576525 287754 503601 791017 896572 454152 594485 663081 365456 830470 772278 794429 953671 916338 561421 293515 254259 573580 094948 591800 > 32¹⁰¹ [i]