MinT - Best Known (78−61, 78, s)-Nets in Base 16

Best Known (78−61, 78, s)-Nets in Base 16

(78−61, 78, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 78, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 78, 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]

(78−61, 78, 112)-Net over F₁₆ — Digital

Digital (17, 78, 112)-net over F₁₆, using

net from sequence [i] based on digital (17, 111)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 17 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(78−61, 78, 972)-Net in Base 16 — Upper bound on s

There is no (17, 78, 973)-net in base 16, because

1 times m-reduction [i] would yield (17, 77, 973)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 525 588459 638070 777173 337889 220994 222061 314686 829477 900400 307847 487736 890647 262410 498933 666976 > 16⁷⁷ [i]