MinT - Best Known (171−41, 171, s)-Nets in Base 4

Best Known (171−41, 171, s)-Nets in Base 4

(171−41, 171, 1032)-Net over F₄ — Constructive and digital

Digital (130, 171, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (130, 172, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 43, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(171−41, 171, 1990)-Net over F₄ — Digital

Digital (130, 171, 1990)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−41, 171, 362806)-Net in Base 4 — Upper bound on s

There is no (130, 171, 362807)-net in base 4, because

1 times m-reduction [i] would yield (130, 170, 362807)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 239755 749581 400558 657530 783803 359174 054274 210814 302307 046932 340612 186180 715904 081045 864120 795532 764609 > 4¹⁷⁰ [i]