MinT - Best Known (28, 28+80, s)-Nets in Base 16

Best Known (28, 28+80, s)-Nets in Base 16

(28, 28+80, 65)-Net over F₁₆ — Constructive and digital

Digital (28, 108, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 108, 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]

(28, 28+80, 76)-Net in Base 16 — Constructive

(28, 108, 76)-net in base 16, using

7 times m-reduction [i] based on (28, 115, 76)-net in base 16, using
- base change [i] based on digital (5, 92, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(28, 28+80, 156)-Net over F₁₆ — Digital

Digital (28, 108, 156)-net over F₁₆, using

t-expansion [i] based on digital (27, 108, 156)-net over F₁₆, using
- net from sequence [i] based on digital (27, 155)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 27 and N(F) ≥ 156, using
    - a curve from the manYPoints database [i]

(28, 28+80, 1852)-Net in Base 16 — Upper bound on s

There is no (28, 108, 1853)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11297 936414 331446 635845 111301 674172 292379 334263 685086 772823 201807 773311 139069 668809 540184 818183 396856 829661 424766 748453 145516 833551 > 16¹⁰⁸ [i]