MinT - Best Known (74−59, 74, s)-Nets in Base 16

Best Known (74−59, 74, s)-Nets in Base 16

(74−59, 74, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 74, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 74, 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]

(74−59, 74, 98)-Net over F₁₆ — Digital

Digital (15, 74, 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]

(74−59, 74, 819)-Net in Base 16 — Upper bound on s

There is no (15, 74, 820)-net in base 16, because

1 times m-reduction [i] would yield (15, 73, 820)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 7978 849213 611949 125742 994207 523907 930324 146042 177264 179970 542406 775203 393351 751385 479576 > 16⁷³ [i]