MinT - Best Known (205−49, 205, s)-Nets in Base 4

Best Known (205−49, 205, s)-Nets in Base 4

(205−49, 205, 1036)-Net over F₄ — Constructive and digital

Digital (156, 205, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (155, 204, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 51, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(205−49, 205, 2352)-Net over F₄ — Digital

Digital (156, 205, 2352)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−49, 205, 428283)-Net in Base 4 — Upper bound on s

There is no (156, 205, 428284)-net in base 4, because

1 times m-reduction [i] would yield (156, 204, 428284)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 661 063830 230828 155385 895242 762650 432738 735758 342016 533085 448583 146934 619805 955329 853646 657875 161541 222371 170880 408682 074731 > 4²⁰⁴ [i]