MinT - Best Known (174−70, 174, s)-Nets in Base 4

Best Known (174−70, 174, s)-Nets in Base 4

(174−70, 174, 130)-Net over F₄ — Constructive and digital

Digital (104, 174, 130)-net over F₄, using

22 times m-reduction [i] based on digital (104, 196, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 98, 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]

(174−70, 174, 254)-Net over F₄ — Digital

Digital (104, 174, 254)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−70, 174, 4534)-Net in Base 4 — Upper bound on s

There is no (104, 174, 4535)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 576 459579 951349 147599 260061 294373 407638 920021 223756 997751 112620 653563 689502 106996 305868 096629 292598 382080 > 4¹⁷⁴ [i]