MinT - Best Known (190−87, 190, s)-Nets in Base 4

Best Known (190−87, 190, s)-Nets in Base 4

(190−87, 190, 130)-Net over F₄ — Constructive and digital

Digital (103, 190, 130)-net over F₄, using

4 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]

(190−87, 190, 181)-Net over F₄ — Digital

Digital (103, 190, 181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−87, 190, 2457)-Net in Base 4 — Upper bound on s

There is no (103, 190, 2458)-net in base 4, because

1 times m-reduction [i] would yield (103, 189, 2458)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 624016 185021 623033 136841 030573 890286 638152 478949 111602 485033 004162 884576 073856 983488 045248 848620 418860 262405 468640 > 4¹⁸⁹ [i]