MinT - Best Known (172, 172+46, s)-Nets in Base 4

Best Known (172, 172+46, s)-Nets in Base 4

(172, 172+46, 1060)-Net over F₄ — Constructive and digital

Digital (172, 218, 1060)-net over F₄, using

4² times duplication [i] based on digital (170, 216, 1060)-net over F₄, using
- trace code for nets [i] based on digital (8, 54, 265)-net over F₂₅₆, using
  - net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(172, 172+46, 4872)-Net over F₄ — Digital

Digital (172, 218, 4872)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+46, 1598864)-Net in Base 4 — Upper bound on s

There is no (172, 218, 1598865)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 177452 592290 494866 098803 821831 238891 700555 095880 258251 161057 449511 554563 202397 096738 932575 300521 879101 909030 912658 022883 833507 332736 > 4²¹⁸ [i]