MinT - Best Known (233−73, 233, s)-Nets in Base 4

Best Known (233−73, 233, s)-Nets in Base 4

(233−73, 233, 450)-Net over F₄ — Constructive and digital

Digital (160, 233, 450)-net over F₄, using

7 times m-reduction [i] based on digital (160, 240, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 120, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(233−73, 233, 795)-Net over F₄ — Digital

Digital (160, 233, 795)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−73, 233, 36074)-Net in Base 4 — Upper bound on s

There is no (160, 233, 36075)-net in base 4, because

1 times m-reduction [i] would yield (160, 232, 36075)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 646837 011328 468169 113290 617784 915582 788588 164084 264555 739744 922720 832404 879319 727745 666262 097359 720817 223877 864219 391754 888775 210604 179790 > 4²³² [i]