MinT - Best Known (179−43, 179, s)-Nets in Base 4

Best Known (179−43, 179, s)-Nets in Base 4

(179−43, 179, 1032)-Net over F₄ — Constructive and digital

Digital (136, 179, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (136, 180, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 45, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(179−43, 179, 2047)-Net over F₄ — Digital

Digital (136, 179, 2047)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−43, 179, 366881)-Net in Base 4 — Upper bound on s

There is no (136, 179, 366882)-net in base 4, because

1 times m-reduction [i] would yield (136, 178, 366882)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 146784 270695 318960 202109 541511 505020 380808 944040 565821 097573 403720 687011 113734 187038 205277 010307 664325 867608 > 4¹⁷⁸ [i]