MinT - Best Known (13, 13+81, s)-Nets in Base 32

Best Known (13, 13+81, s)-Nets in Base 32

(13, 13+81, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 94, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 94, 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]

(13, 13+81, 129)-Net over F₃₂ — Digital

Digital (13, 94, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 94, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(13, 13+81, 1585)-Net in Base 32 — Upper bound on s

There is no (13, 94, 1586)-net in base 32, because

1 times m-reduction [i] would yield (13, 93, 1586)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 95 624535 772817 987307 423840 921975 116414 442232 138123 591781 711266 095470 768270 550236 771642 547603 619832 368318 166987 776563 985718 680071 160460 874930 > 32⁹³ [i]