MinT - Best Known (129−95, 129, s)-Nets in Base 16

Best Known (129−95, 129, s)-Nets in Base 16

(129−95, 129, 65)-Net over F₁₆ — Constructive and digital

Digital (34, 129, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 129, 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]

(129−95, 129, 98)-Net in Base 16 — Constructive

(34, 129, 98)-net in base 16, using

t-expansion [i] based on (33, 129, 98)-net in base 16, using
- 1 times m-reduction [i] based on (33, 130, 98)-net in base 16, using
  - base change [i] based on digital (7, 104, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
        a function field by SÃ©mirat [i]

(129−95, 129, 193)-Net over F₁₆ — Digital

Digital (34, 129, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 129, 193)-net over F₁₆, using
- net from sequence [i] based on digital (33, 192)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 33 and N(F) ≥ 193, using
    - a curve from the manYPoints database [i]

(129−95, 129, 2303)-Net in Base 16 — Upper bound on s

There is no (34, 129, 2304)-net in base 16, because

1 times m-reduction [i] would yield (34, 128, 2304)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13486 061642 547423 670823 043045 949024 463987 453190 332066 032995 082326 900442 096332 829893 821556 065934 231650 239781 891097 725534 661911 624381 495541 903932 702999 485321 > 16¹²⁸ [i]