MinT - Best Known (162−38, 162, s)-Nets in Base 4

Best Known (162−38, 162, s)-Nets in Base 4

(162−38, 162, 1036)-Net over F₄ — Constructive and digital

Digital (124, 162, 1036)-net over F₄, using

4² times duplication [i] based on digital (122, 160, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 40, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(162−38, 162, 2131)-Net over F₄ — Digital

Digital (124, 162, 2131)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−38, 162, 359276)-Net in Base 4 — Upper bound on s

There is no (124, 162, 359277)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 175924 129295 477156 219521 244608 805709 809879 366867 532574 596081 172346 060435 973610 592734 879473 693576 > 4¹⁶² [i]