MinT - Best Known (181−43, 181, s)-Nets in Base 4

Best Known (181−43, 181, s)-Nets in Base 4

(181−43, 181, 1036)-Net over F₄ — Constructive and digital

Digital (138, 181, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (137, 180, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 45, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(181−43, 181, 2185)-Net over F₄ — Digital

Digital (138, 181, 2185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−43, 181, 418666)-Net in Base 4 — Upper bound on s

There is no (138, 181, 418667)-net in base 4, because

1 times m-reduction [i] would yield (138, 180, 418667)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 348638 033091 404283 861041 130292 549303 505839 660959 386682 820983 239497 205784 015570 968430 996079 982191 733689 879448 > 4¹⁸⁰ [i]