MinT - Best Known (7, 7+37, s)-Nets in Base 16

Best Known (7, 7+37, s)-Nets in Base 16

(7, 7+37, 65)-Net over F₁₆ — Constructive and digital

Digital (7, 44, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 44, 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]

(7, 7+37, 369)-Net in Base 16 — Upper bound on s

There is no (7, 44, 370)-net in base 16, because

1 times m-reduction [i] would yield (7, 43, 370)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6193 292331 819747 248598 609890 723338 806761 816669 369776 > 16⁴³ [i]