MinT - Best Known (245−57, 245, s)-Nets in Base 4

Best Known (245−57, 245, s)-Nets in Base 4

(245−57, 245, 1044)-Net over F₄ — Constructive and digital

Digital (188, 245, 1044)-net over F₄, using

4¹ times duplication [i] based on digital (187, 244, 1044)-net over F₄, using
- trace code for nets [i] based on digital (4, 61, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(245−57, 245, 3143)-Net over F₄ — Digital

Digital (188, 245, 3143)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−57, 245, 664341)-Net in Base 4 — Upper bound on s

There is no (188, 245, 664342)-net in base 4, because

1 times m-reduction [i] would yield (188, 244, 664342)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 799 171728 289859 626886 573044 387338 264809 092184 292195 011009 558290 355915 865813 566894 026312 070423 267426 238089 797591 809639 377984 018288 759892 578376 230944 > 4²⁴⁴ [i]