MinT - Best Known (175−72, 175, s)-Nets in Base 4

Best Known (175−72, 175, s)-Nets in Base 4

(175−72, 175, 130)-Net over F₄ — Constructive and digital

Digital (103, 175, 130)-net over F₄, using

19 times m-reduction [i] based on digital (103, 194, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 97, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(175−72, 175, 237)-Net over F₄ — Digital

Digital (103, 175, 237)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−72, 175, 3991)-Net in Base 4 — Upper bound on s

There is no (103, 175, 3992)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2309 293064 859178 776459 416101 992323 853813 125715 442859 631645 968771 417341 926256 162568 888129 994933 099726 740020 > 4¹⁷⁵ [i]