MinT - Best Known (147−43, 147, s)-Nets in Base 4

Best Known (147−43, 147, s)-Nets in Base 4

(147−43, 147, 384)-Net over F₄ — Constructive and digital

Digital (104, 147, 384)-net over F₄, using

t-expansion [i] based on digital (103, 147, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 49, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(147−43, 147, 720)-Net over F₄ — Digital

Digital (104, 147, 720)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−43, 147, 44356)-Net in Base 4 — Upper bound on s

There is no (104, 147, 44357)-net in base 4, because

1 times m-reduction [i] would yield (104, 146, 44357)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7959 798615 234525 855039 976847 204331 724709 354901 181939 518132 156139 214562 782022 257131 144048 > 4¹⁴⁶ [i]