MinT - Best Known (212−51, 212, s)-Nets in Base 4

Best Known (212−51, 212, s)-Nets in Base 4

(212−51, 212, 1036)-Net over F₄ — Constructive and digital

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]

(212−51, 212, 2344)-Net over F₄ — Digital

Digital (161, 212, 2344)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−51, 212, 409137)-Net in Base 4 — Upper bound on s

There is no (161, 212, 409138)-net in base 4, because

1 times m-reduction [i] would yield (161, 211, 409138)-net in base 4, but
- 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]