MinT - Best Known (209−50, 209, s)-Nets in Base 4

Best Known (209−50, 209, s)-Nets in Base 4

(209−50, 209, 1036)-Net over F₄ — Constructive and digital

Digital (159, 209, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (158, 208, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 52, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(209−50, 209, 2380)-Net over F₄ — Digital

Digital (159, 209, 2380)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−50, 209, 366186)-Net in Base 4 — Upper bound on s

There is no (159, 209, 366187)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 676957 800903 634262 117065 671392 584474 451227 773380 059542 249856 755793 126143 736416 624937 739734 259117 116693 423349 459054 772168 535180 > 4²⁰⁹ [i]