MinT - Best Known (249−58, 249, s)-Nets in Base 4

Best Known (249−58, 249, s)-Nets in Base 4

(249−58, 249, 1044)-Net over F₄ — Constructive and digital

Digital (191, 249, 1044)-net over F₄, using

4¹ times duplication [i] based on digital (190, 248, 1044)-net over F₄, using
- trace code for nets [i] based on digital (4, 62, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(249−58, 249, 3168)-Net over F₄ — Digital

Digital (191, 249, 3168)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−58, 249, 574638)-Net in Base 4 — Upper bound on s

There is no (191, 249, 574639)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 818378 270350 481368 782455 391827 318086 155879 036146 920550 484449 971363 008563 671936 106485 094838 532635 310738 591870 401777 897246 370094 801410 936510 123540 361356 > 4²⁴⁹ [i]