MinT - Best Known (186, 186+59, s)-Nets in Base 4

Best Known (186, 186+59, s)-Nets in Base 4

(186, 186+59, 1036)-Net over F₄ — Constructive and digital

Digital (186, 245, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (185, 244, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 61, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(186, 186+59, 2643)-Net over F₄ — Digital

Digital (186, 245, 2643)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 186+59, 452466)-Net in Base 4 — Upper bound on s

There is no (186, 245, 452467)-net in base 4, because

1 times m-reduction [i] would yield (186, 244, 452467)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 799 202247 520718 168685 541808 010070 819487 862591 931667 886000 884657 419279 778395 747706 565897 772501 307181 844923 647561 399650 533214 955813 167327 038484 284592 > 4²⁴⁴ [i]