MinT - Best Known (16, 16+87, s)-Nets in Base 32

Best Known (16, 16+87, s)-Nets in Base 32

(16, 16+87, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 103, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 103, 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+87, 158)-Net over F₃₂ — Digital

Digital (16, 103, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 103, 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+87, 2002)-Net in Base 32 — Upper bound on s

There is no (16, 103, 2003)-net in base 32, because

1 times m-reduction [i] would yield (16, 102, 2003)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3363 298195 167580 925726 844557 903615 627937 175757 946901 807124 380766 926868 407817 648422 375279 135473 238074 337188 742060 785866 116601 391026 315665 540813 222931 020128 > 32¹⁰² [i]