MinT - Best Known (143−33, 143, s)-Nets in Base 4

Best Known (143−33, 143, s)-Nets in Base 4

(143−33, 143, 1036)-Net over F₄ — Constructive and digital

Digital (110, 143, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (110, 144, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 36, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(143−33, 143, 2106)-Net over F₄ — Digital

Digital (110, 143, 2106)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−33, 143, 499676)-Net in Base 4 — Upper bound on s

There is no (110, 143, 499677)-net in base 4, because

1 times m-reduction [i] would yield (110, 142, 499677)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 083412 673944 792546 095866 954658 350431 991156 086316 672950 787838 163175 213040 517387 171303 > 4¹⁴² [i]