MinT - Best Known (130−59, 130, s)-Nets in Base 4

Best Known (130−59, 130, s)-Nets in Base 4

(130−59, 130, 130)-Net over F₄ — Constructive and digital

Digital (71, 130, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 65, 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]

(130−59, 130, 135)-Net over F₄ — Digital

Digital (71, 130, 135)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−59, 130, 1830)-Net in Base 4 — Upper bound on s

There is no (71, 130, 1831)-net in base 4, because

1 times m-reduction [i] would yield (71, 129, 1831)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 466556 314011 872671 140471 907307 040077 356798 596069 674574 588561 709213 569776 514328 > 4¹²⁹ [i]