MinT - Best Known (93−63, 93, s)-Nets in Base 16

Best Known (93−63, 93, s)-Nets in Base 16

(93−63, 93, 65)-Net over F₁₆ — Constructive and digital

Digital (30, 93, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 93, 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]

(93−63, 93, 120)-Net in Base 16 — Constructive

(30, 93, 120)-net in base 16, using

2 times m-reduction [i] based on (30, 95, 120)-net in base 16, using
- base change [i] based on digital (11, 76, 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]

(93−63, 93, 162)-Net over F₁₆ — Digital

Digital (30, 93, 162)-net over F₁₆, using

net from sequence [i] based on digital (30, 161)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 30 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(93−63, 93, 3083)-Net in Base 16 — Upper bound on s

There is no (30, 93, 3084)-net in base 16, because

1 times m-reduction [i] would yield (30, 92, 3084)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 603 322216 311222 400925 647134 161513 271387 965256 888602 845217 570415 600533 159656 506323 408710 821666 930100 562363 335936 > 16⁹² [i]