MinT - Best Known (162−37, 162, s)-Nets in Base 4

Best Known (162−37, 162, s)-Nets in Base 4

(162−37, 162, 1040)-Net over F₄ — Constructive and digital

Digital (125, 162, 1040)-net over F₄, using

4² times duplication [i] based on digital (123, 160, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 40, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(162−37, 162, 2455)-Net over F₄ — Digital

Digital (125, 162, 2455)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−37, 162, 611069)-Net in Base 4 — Upper bound on s

There is no (125, 162, 611070)-net in base 4, because

1 times m-reduction [i] would yield (125, 161, 611070)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 544061 950792 461547 381460 262872 464657 197569 094890 826496 941762 529926 205251 562845 706103 209082 521622 > 4¹⁶¹ [i]