MinT - Best Known (114−95, 114, s)-Nets in Base 16

Best Known (114−95, 114, s)-Nets in Base 16

(114−95, 114, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 114, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 114, 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]

(114−95, 114, 129)-Net over F₁₆ — Digital

Digital (19, 114, 129)-net over F₁₆, using

net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(114−95, 114, 935)-Net in Base 16 — Upper bound on s

There is no (19, 114, 936)-net in base 16, because

1 times m-reduction [i] would yield (19, 113, 936)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11802 758237 123186 027082 097969 002029 516653 675424 903975 946579 397251 656099 994484 580393 531483 072008 663837 821790 085824 246576 196064 156664 395856 > 16¹¹³ [i]