MinT - Best Known (49−21, 49, s)-Nets in Base 4

Best Known (49−21, 49, s)-Nets in Base 4

(49−21, 49, 76)-Net over F₄ — Constructive and digital

Digital (28, 49, 76)-net over F₄, using

1 times m-reduction [i] based on digital (28, 50, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 25, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(49−21, 49, 78)-Net over F₄ — Digital

Digital (28, 49, 78)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(49−21, 49, 1163)-Net in Base 4 — Upper bound on s

There is no (28, 49, 1164)-net in base 4, because

1 times m-reduction [i] would yield (28, 48, 1164)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 79438 663208 876343 141540 008683 > 4⁴⁸ [i]