MinT - Best Known (147−45, 147, s)-Nets in Base 4

Best Known (147−45, 147, s)-Nets in Base 4

(147−45, 147, 312)-Net over F₄ — Constructive and digital

Digital (102, 147, 312)-net over F₄, using

t-expansion [i] based on digital (101, 147, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 49, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(147−45, 147, 593)-Net over F₄ — Digital

Digital (102, 147, 593)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−45, 147, 29851)-Net in Base 4 — Upper bound on s

There is no (102, 147, 29852)-net in base 4, because

1 times m-reduction [i] would yield (102, 146, 29852)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7961 983670 560812 768459 196600 496949 113610 253285 138719 535856 163382 761277 248165 964500 030730 > 4¹⁴⁶ [i]