MinT - Best Known (66, 66+47, s)-Nets in Base 4

Best Known (66, 66+47, s)-Nets in Base 4

(66, 66+47, 130)-Net over F₄ — Constructive and digital

Digital (66, 113, 130)-net over F₄, using

7 times m-reduction [i] based on digital (66, 120, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 60, 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]

(66, 66+47, 159)-Net over F₄ — Digital

Digital (66, 113, 159)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+47, 2667)-Net in Base 4 — Upper bound on s

There is no (66, 113, 2668)-net in base 4, because

1 times m-reduction [i] would yield (66, 112, 2668)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27 103548 262704 597600 388620 744712 200175 121858 390206 075860 491870 268700 > 4¹¹² [i]