MinT - Best Known (63, 63+39, s)-Nets in Base 4

Best Known (63, 63+39, s)-Nets in Base 4

(63, 63+39, 130)-Net over F₄ — Constructive and digital

Digital (63, 102, 130)-net over F₄, using

12 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+39, 194)-Net over F₄ — Digital

Digital (63, 102, 194)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+39, 4177)-Net in Base 4 — Upper bound on s

There is no (63, 102, 4178)-net in base 4, because

1 times m-reduction [i] would yield (63, 101, 4178)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 438651 757675 967904 117181 856410 861055 407110 736862 072813 665264 > 4¹⁰¹ [i]