MinT - Best Known (94−78, 94, s)-Nets in Base 16

Best Known (94−78, 94, s)-Nets in Base 16

(94−78, 94, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 94, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 94, 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]

(94−78, 94, 98)-Net over F₁₆ — Digital

Digital (16, 94, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 94, 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]

(94−78, 94, 798)-Net in Base 16 — Upper bound on s

There is no (16, 94, 799)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 160770 347366 655342 911572 648509 717980 651894 936969 883617 070592 890166 584778 410715 025209 060756 643482 848927 632042 852416 > 16⁹⁴ [i]