MinT - Best Known (158−36, 158, s)-Nets in Base 4

Best Known (158−36, 158, s)-Nets in Base 4

(158−36, 158, 1040)-Net over F₄ — Constructive and digital

Digital (122, 158, 1040)-net over F₄, using

4² times duplication [i] based on digital (120, 156, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 39, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(158−36, 158, 2438)-Net over F₄ — Digital

Digital (122, 158, 2438)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−36, 158, 485003)-Net in Base 4 — Upper bound on s

There is no (122, 158, 485004)-net in base 4, because

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]