MinT - Best Known (211−50, 211, s)-Nets in Base 4

Best Known (211−50, 211, s)-Nets in Base 4

(211−50, 211, 1036)-Net over F₄ — Constructive and digital

Digital (161, 211, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (161, 212, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 53, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(211−50, 211, 2517)-Net over F₄ — Digital

Digital (161, 211, 2517)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−50, 211, 409137)-Net in Base 4 — Upper bound on s

There is no (161, 211, 409138)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 831053 497027 135572 986238 015931 341923 932002 532165 937195 358524 691325 479948 053208 009447 718148 794696 743955 999186 208667 654152 144484 > 4²¹¹ [i]