MinT - Best Known (126−113, 126, s)-Nets in Base 16

Best Known (126−113, 126, s)-Nets in Base 16

(126−113, 126, 65)-Net over F₁₆ — Constructive and digital

Digital (13, 126, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 126, 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]

(126−113, 126, 97)-Net over F₁₆ — Digital

Digital (13, 126, 97)-net over F₁₆, using

net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
  - a curve from the manYPoints database [i]

(126−113, 126, 640)-Net in Base 16 — Upper bound on s

There is no (13, 126, 641)-net in base 16, because

31 times m-reduction [i] would yield (13, 95, 641)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 465550 478621 157356 149048 290016 113849 140183 928334 549424 044960 758861 294765 988499 458227 868502 028128 792089 678111 001216 > 16⁹⁵ [i]