MinT - Best Known (14, 14+89, s)-Nets in Base 32

Best Known (14, 14+89, s)-Nets in Base 32

(14, 14+89, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 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]

(14, 14+89, 146)-Net over F₃₂ — Digital

Digital (14, 103, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(14, 14+89, 1694)-Net in Base 32 — Upper bound on s

There is no (14, 103, 1695)-net in base 32, because

1 times m-reduction [i] would yield (14, 102, 1695)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3425 412560 401838 720535 115719 577171 673879 200002 484832 280373 522446 098943 031546 058215 437972 437545 894281 913402 425179 055139 943418 833601 347939 043347 408530 822132 > 32¹⁰² [i]