MinT - Best Known (159−37, 159, s)-Nets in Base 4

Best Known (159−37, 159, s)-Nets in Base 4

(159−37, 159, 1036)-Net over F₄ — Constructive and digital

Digital (122, 159, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (122, 160, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 40, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(159−37, 159, 2189)-Net over F₄ — Digital

Digital (122, 159, 2189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−37, 159, 485003)-Net in Base 4 — Upper bound on s

There is no (122, 159, 485004)-net in base 4, because

1 times m-reduction [i] would yield (122, 158, 485004)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 133503 003632 971161 054643 081310 132906 581842 059888 596744 476064 258525 812742 122735 096569 821462 701688 > 4¹⁵⁸ [i]