MinT - Best Known (180, 180+53, s)-Nets in Base 4

Best Known (180, 180+53, s)-Nets in Base 4

(180, 180+53, 1048)-Net over F₄ — Constructive and digital

Digital (180, 233, 1048)-net over F₄, using

4¹ times duplication [i] based on digital (179, 232, 1048)-net over F₄, using
- trace code for nets [i] based on digital (5, 58, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(180, 180+53, 3387)-Net over F₄ — Digital

Digital (180, 233, 3387)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+53, 828682)-Net in Base 4 — Upper bound on s

There is no (180, 233, 828683)-net in base 4, because

1 times m-reduction [i] would yield (180, 232, 828683)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 634452 380545 202403 253590 624004 406090 787535 982561 155999 427949 879079 141603 056386 290732 710773 824708 936825 488335 171339 881330 970526 481432 811600 > 4²³² [i]