MinT - Best Known (18, 78, s)-Nets in Base 16

Best Known (18, 78, s)-Nets in Base 16

(18, 78, 65)-Net over F₁₆ — Constructive and digital

Digital (18, 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]

(18, 78, 113)-Net over F₁₆ — Digital

Digital (18, 78, 113)-net over F₁₆, using

net from sequence [i] based on digital (18, 112)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 18 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(18, 78, 1068)-Net in Base 16 — Upper bound on s

There is no (18, 78, 1069)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 8457 062359 919118 861083 089207 082309 146471 059119 703886 600344 478478 459691 071299 757224 620726 524176 > 16⁷⁸ [i]