MinT - Best Known (135, 135+50, s)-Nets in Base 4

Best Known (135, 135+50, s)-Nets in Base 4

(135, 135+50, 531)-Net over F₄ — Constructive and digital

Digital (135, 185, 531)-net over F₄, using

7 times m-reduction [i] based on digital (135, 192, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 64, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(135, 135+50, 1219)-Net over F₄ — Digital

Digital (135, 185, 1219)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+50, 96751)-Net in Base 4 — Upper bound on s

There is no (135, 185, 96752)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2405 281007 070646 107859 618187 199286 939900 509737 464763 173856 462402 413415 423232 741647 452264 631374 526865 482925 097234 > 4¹⁸⁵ [i]