MinT - Best Known (63, 63+49, s)-Nets in Base 4

Best Known (63, 63+49, s)-Nets in Base 4

(63, 63+49, 130)-Net over F₄ — Constructive and digital

Digital (63, 112, 130)-net over F₄, using

2 times m-reduction [i] based on digital (63, 114, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 57, 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]

(63, 63+49, 134)-Net over F₄ — Digital

Digital (63, 112, 134)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+49, 1970)-Net in Base 4 — Upper bound on s

There is no (63, 112, 1971)-net in base 4, because

1 times m-reduction [i] would yield (63, 111, 1971)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 806330 372620 609789 600136 982427 768130 806677 810777 337393 659350 104636 > 4¹¹¹ [i]