MinT - Best Known (46, 46+29, s)-Nets in Base 4

Best Known (46, 46+29, s)-Nets in Base 4

(46, 46+29, 130)-Net over F₄ — Constructive and digital

Digital (46, 75, 130)-net over F₄, using

5 times m-reduction [i] based on digital (46, 80, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 40, 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]

(46, 46+29, 147)-Net over F₄ — Digital

Digital (46, 75, 147)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+29, 3055)-Net in Base 4 — Upper bound on s

There is no (46, 75, 3056)-net in base 4, because

1 times m-reduction [i] would yield (46, 74, 3056)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 357 751233 655771 978878 595942 247444 435698 263955 > 4⁷⁴ [i]