MinT - Best Known (94−75, 94, s)-Nets in Base 16

Best Known (94−75, 94, s)-Nets in Base 16

(94−75, 94, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 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]

(94−75, 94, 129)-Net over F₁₆ — Digital

Digital (19, 94, 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]

(94−75, 94, 1018)-Net in Base 16 — Upper bound on s

There is no (19, 94, 1019)-net in base 16, because

1 times m-reduction [i] would yield (19, 93, 1019)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9933 155901 669297 225538 938750 218708 276143 899646 291177 150074 496033 644337 063169 741609 851365 097539 992839 254707 430796 > 16⁹³ [i]