MinT - Best Known (48−20, 48, s)-Nets in Base 4

Best Known (48−20, 48, s)-Nets in Base 4

(48−20, 48, 90)-Net over F₄ — Constructive and digital

Digital (28, 48, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 24, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(48−20, 48, 1163)-Net in Base 4 — Upper bound on s

There is no (28, 48, 1164)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 79438 663208 876343 141540 008683 > 4⁴⁸ [i]