MinT - Best Known (13, 13+69, s)-Nets in Base 32

Best Known (13, 13+69, s)-Nets in Base 32

(13, 13+69, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 82, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 82, 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+69, 129)-Net over F₃₂ — Digital

Digital (13, 82, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 82, 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+69, 1664)-Net in Base 32 — Upper bound on s

There is no (13, 82, 1665)-net in base 32, because

1 times m-reduction [i] would yield (13, 81, 1665)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 83 005517 582538 299388 154207 063315 158986 005561 461314 813316 723087 888349 843728 716414 638242 286436 196974 829570 997535 900458 156992 > 32⁸¹ [i]