MinT - Best Known (227−46, 227, s)-Nets in Base 4

Best Known (227−46, 227, s)-Nets in Base 4

(227−46, 227, 1539)-Net over F₄ — Constructive and digital

Digital (181, 227, 1539)-net over F₄, using

t-expansion [i] based on digital (180, 227, 1539)-net over F₄, using
- 1 times m-reduction [i] based on digital (180, 228, 1539)-net over F₄, using
  - trace code for nets [i] based on digital (28, 76, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(227−46, 227, 6421)-Net over F₄ — Digital

Digital (181, 227, 6421)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−46, 227, 2750441)-Net in Base 4 — Upper bound on s

There is no (181, 227, 2750442)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46517 837658 572530 655640 590325 946777 667968 929968 145178 123840 202437 973360 793898 626867 806513 127098 573831 057604 495730 046971 964670 065455 146712 > 4²²⁷ [i]