MinT - Best Known (187−45, 187, s)-Nets in Base 4

Best Known (187−45, 187, s)-Nets in Base 4

(187−45, 187, 1032)-Net over F₄ — Constructive and digital

Digital (142, 187, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (142, 188, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 47, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(187−45, 187, 2104)-Net over F₄ — Digital

Digital (142, 187, 2104)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−45, 187, 371410)-Net in Base 4 — Upper bound on s

There is no (142, 187, 371411)-net in base 4, because

1 times m-reduction [i] would yield (142, 186, 371411)-net in base 4, but
- 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]