MinT - Best Known (189, 189+56, s)-Nets in Base 4

Best Known (189, 189+56, s)-Nets in Base 4

(189, 189+56, 1048)-Net over F₄ — Constructive and digital

Digital (189, 245, 1048)-net over F₄, using

4¹ times duplication [i] based on digital (188, 244, 1048)-net over F₄, using
- trace code for nets [i] based on digital (5, 61, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(189, 189+56, 3447)-Net over F₄ — Digital

Digital (189, 245, 3447)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(189, 189+56, 698062)-Net in Base 4 — Upper bound on s

There is no (189, 245, 698063)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3196 696433 432521 888372 101614 544045 207956 077648 696558 975959 873945 449831 470883 565957 509845 434656 293359 853158 980297 755330 054117 813921 386470 037526 942900 > 4²⁴⁵ [i]