MinT - Best Known (138, 138+44, s)-Nets in Base 4

Best Known (138, 138+44, s)-Nets in Base 4

(138, 138+44, 1032)-Net over F₄ — Constructive and digital

Digital (138, 182, 1032)-net over F₄, using

4² times duplication [i] based on digital (136, 180, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 45, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(138, 138+44, 2010)-Net over F₄ — Digital

Digital (138, 182, 2010)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+44, 288657)-Net in Base 4 — Upper bound on s

There is no (138, 182, 288658)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 577719 249344 503252 571446 547682 302475 210326 738163 770273 289158 722691 006810 197144 537996 779682 198066 677542 916672 > 4¹⁸² [i]