MinT - Best Known (106−91, 106, s)-Nets in Base 16

Best Known (106−91, 106, s)-Nets in Base 16

(106−91, 106, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 106, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 106, 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]

(106−91, 106, 98)-Net over F₁₆ — Digital

Digital (15, 106, 98)-net over F₁₆, using

net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(106−91, 106, 733)-Net in Base 16 — Upper bound on s

There is no (15, 106, 734)-net in base 16, because

1 times m-reduction [i] would yield (15, 105, 734)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 831216 395903 212279 438361 429958 056234 484606 357042 290580 283983 917380 771759 452237 374026 250472 067105 829517 255117 332927 479107 372326 > 16¹⁰⁵ [i]