MinT - Best Known (189−85, 189, s)-Nets in Base 4

Best Known (189−85, 189, s)-Nets in Base 4

(189−85, 189, 130)-Net over F₄ — Constructive and digital

Digital (104, 189, 130)-net over F₄, using

7 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]

(189−85, 189, 191)-Net over F₄ — Digital

Digital (104, 189, 191)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−85, 189, 2692)-Net in Base 4 — Upper bound on s

There is no (104, 189, 2693)-net in base 4, because

1 times m-reduction [i] would yield (104, 188, 2693)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 155748 347666 828934 496378 533856 484050 220769 750009 921354 100563 805677 589771 221120 338852 191664 657228 740596 340074 050080 > 4¹⁸⁸ [i]