MinT - Best Known (228−46, 228, s)-Nets in Base 4

Best Known (228−46, 228, s)-Nets in Base 4

(228−46, 228, 1539)-Net over F₄ — Constructive and digital

Digital (182, 228, 1539)-net over F₄, using

3 times m-reduction [i] based on digital (182, 231, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 77, 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]

(228−46, 228, 6621)-Net over F₄ — Digital

Digital (182, 228, 6621)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−46, 228, 2921319)-Net in Base 4 — Upper bound on s

There is no (182, 228, 2921320)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186070 828690 740245 398872 523805 989182 874568 002907 798174 416789 635587 392249 804122 970463 570785 070127 331729 800260 499620 336614 019956 166084 127334 > 4²²⁸ [i]