MinT - Best Known (32, 32+73, s)-Nets in Base 16

Best Known (32, 32+73, s)-Nets in Base 16

(32, 32+73, 65)-Net over F₁₆ — Constructive and digital

Digital (32, 105, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 105, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(32, 32+73, 120)-Net in Base 16 — Constructive

(32, 105, 120)-net in base 16, using

base change [i] based on digital (11, 84, 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]

(32, 32+73, 168)-Net over F₁₆ — Digital

Digital (32, 105, 168)-net over F₁₆, using

t-expansion [i] based on digital (31, 105, 168)-net over F₁₆, using
- net from sequence [i] based on digital (31, 167)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 31 and N(F) ≥ 168, using
    - a curve from the manYPoints database [i]

(32, 32+73, 2845)-Net in Base 16 — Upper bound on s

There is no (32, 105, 2846)-net in base 16, because

1 times m-reduction [i] would yield (32, 104, 2846)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 169808 619202 052899 378109 366642 791967 555375 685557 243131 719454 873562 776206 900556 393132 779603 024940 294867 517816 295056 852240 794216 > 16¹⁰⁴ [i]