MinT - Best Known (129−39, 129, s)-Nets in Base 4

Best Known (129−39, 129, s)-Nets in Base 4

(129−39, 129, 312)-Net over F₄ — Constructive and digital

Digital (90, 129, 312)-net over F₄, using

t-expansion [i] based on digital (89, 129, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 43, 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]

(129−39, 129, 565)-Net over F₄ — Digital

Digital (90, 129, 565)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−39, 129, 30050)-Net in Base 4 — Upper bound on s

There is no (90, 129, 30051)-net in base 4, because

1 times m-reduction [i] would yield (90, 128, 30051)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 115807 658309 437981 747816 600997 887976 365343 618060 580744 846021 387516 868130 486584 > 4¹²⁸ [i]