MinT - Best Known (245−55, 245, s)-Nets in Base 4

Best Known (245−55, 245, s)-Nets in Base 4

(245−55, 245, 1052)-Net over F₄ — Constructive and digital

Digital (190, 245, 1052)-net over F₄, using

4¹ times duplication [i] based on digital (189, 244, 1052)-net over F₄, using
- trace code for nets [i] based on digital (6, 61, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(245−55, 245, 3794)-Net over F₄ — Digital

Digital (190, 245, 3794)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−55, 245, 1004880)-Net in Base 4 — Upper bound on s

There is no (190, 245, 1004881)-net in base 4, because

1 times m-reduction [i] would yield (190, 244, 1004881)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 799 176930 217462 727142 104652 510583 009081 639085 970216 542499 861185 577858 984787 742730 192660 729311 753024 062857 804694 874392 981971 963618 775449 912528 533824 > 4²⁴⁴ [i]