MinT - Best Known (156, 156+46, s)-Nets in Base 4

Best Known (156, 156+46, s)-Nets in Base 4

(156, 156+46, 1044)-Net over F₄ — Constructive and digital

Digital (156, 202, 1044)-net over F₄, using

4² times duplication [i] based on digital (154, 200, 1044)-net over F₄, using
- trace code for nets [i] based on digital (4, 50, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(156, 156+46, 2985)-Net over F₄ — Digital

Digital (156, 202, 2985)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+46, 609507)-Net in Base 4 — Upper bound on s

There is no (156, 202, 609508)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 316808 930757 215039 269813 677880 151249 550899 678100 934705 449492 272141 813128 344883 439042 340206 093481 649232 111669 220290 130680 > 4²⁰² [i]