MinT - Best Known (102, 102+47, s)-Nets in Base 4

Best Known (102, 102+47, s)-Nets in Base 4

(102, 102+47, 240)-Net over F₄ — Constructive and digital

Digital (102, 149, 240)-net over F₄, using

t-expansion [i] based on digital (101, 149, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (101, 150, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 50, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]

(102, 102+47, 531)-Net over F₄ — Digital

Digital (102, 149, 531)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+47, 23502)-Net in Base 4 — Upper bound on s

There is no (102, 149, 23503)-net in base 4, because

1 times m-reduction [i] would yield (102, 148, 23503)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 127367 346269 621884 522258 382945 006899 070149 764719 501574 570625 987509 663595 402947 821151 636880 > 4¹⁴⁸ [i]