MinT - Best Known (174−74, 174, s)-Nets in Base 4

Best Known (174−74, 174, s)-Nets in Base 4

(174−74, 174, 130)-Net over F₄ — Constructive and digital

Digital (100, 174, 130)-net over F₄, using

14 times m-reduction [i] based on digital (100, 188, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 94, 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]

(174−74, 174, 212)-Net over F₄ — Digital

Digital (100, 174, 212)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−74, 174, 3281)-Net in Base 4 — Upper bound on s

There is no (100, 174, 3282)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 574 373435 761994 689425 639698 534105 406519 314032 307254 689925 132232 462286 538750 098009 823521 692418 496611 928360 > 4¹⁷⁴ [i]