MinT - Best Known (193−39, 193, s)-Nets in Base 4

Best Known (193−39, 193, s)-Nets in Base 4

(193−39, 193, 1064)-Net over F₄ — Constructive and digital

Digital (154, 193, 1064)-net over F₄, using

4¹ times duplication [i] based on digital (153, 192, 1064)-net over F₄, using
- trace code for nets [i] based on digital (9, 48, 266)-net over F₂₅₆, using
  - net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(193−39, 193, 5740)-Net over F₄ — Digital

Digital (154, 193, 5740)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−39, 193, 3206762)-Net in Base 4 — Upper bound on s

There is no (154, 193, 3206763)-net in base 4, because

1 times m-reduction [i] would yield (154, 192, 3206763)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 39 402074 704757 555224 543141 497477 479744 854935 820774 621964 516075 727982 684315 287643 807293 888224 821099 873719 734810 073400 > 4¹⁹² [i]