MinT - Best Known (188−46, 188, s)-Nets in Base 4

Best Known (188−46, 188, s)-Nets in Base 4

(188−46, 188, 1032)-Net over F₄ — Constructive and digital

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]

(188−46, 188, 1947)-Net over F₄ — Digital

Digital (142, 188, 1947)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−46, 188, 262113)-Net in Base 4 — Upper bound on s

There is no (142, 188, 262114)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 153914 933536 776801 833238 653538 872844 104760 496510 748536 544463 643943 790699 364495 748515 744256 493796 248409 308985 488592 > 4¹⁸⁸ [i]