MinT - Best Known (121−29, 121, s)-Nets in Base 4

Best Known (121−29, 121, s)-Nets in Base 4

(121−29, 121, 1032)-Net over F₄ — Constructive and digital

Digital (92, 121, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (91, 120, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 30, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(121−29, 121, 1519)-Net over F₄ — Digital

Digital (92, 121, 1519)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−29, 121, 291631)-Net in Base 4 — Upper bound on s

There is no (92, 121, 291632)-net in base 4, because

1 times m-reduction [i] would yield (92, 120, 291632)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 766910 220427 747637 090216 146572 840742 676733 633931 800134 391052 043939 998635 > 4¹²⁰ [i]