MinT - Best Known (186−44, 186, s)-Nets in Base 4

Best Known (186−44, 186, s)-Nets in Base 4

(186−44, 186, 1036)-Net over F₄ — Constructive and digital

Digital (142, 186, 1036)-net over F₄, using

4² times duplication [i] based on digital (140, 184, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 46, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(186−44, 186, 2284)-Net over F₄ — Digital

Digital (142, 186, 2284)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−44, 186, 371410)-Net in Base 4 — Upper bound on s

There is no (142, 186, 371411)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9619 766156 818468 944164 688122 838927 075080 995916 243607 143824 997821 719021 099319 801451 051864 248449 844932 470313 344176 > 4¹⁸⁶ [i]