MinT - Best Known (163, 163+52, s)-Nets in Base 4

Best Known (163, 163+52, s)-Nets in Base 4

(163, 163+52, 1032)-Net over F₄ — Constructive and digital

Digital (163, 215, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (163, 216, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 54, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(163, 163+52, 2310)-Net over F₄ — Digital

Digital (163, 215, 2310)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+52, 334747)-Net in Base 4 — Upper bound on s

There is no (163, 215, 334748)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2772 779345 586605 009442 486912 543292 844929 473361 648315 981470 553194 913279 767293 521391 238902 311445 696344 692212 902507 643497 893781 543795 > 4²¹⁵ [i]