MinT - Best Known (194, 194+58, s)-Nets in Base 4

Best Known (194, 194+58, s)-Nets in Base 4

(194, 194+58, 1048)-Net over F₄ — Constructive and digital

Digital (194, 252, 1048)-net over F₄, using

trace code for nets [i] based on digital (5, 63, 262)-net over F₂₅₆, using
- net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(194, 194+58, 3406)-Net over F₄ — Digital

Digital (194, 252, 3406)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194, 194+58, 663252)-Net in Base 4 — Upper bound on s

There is no (194, 252, 663253)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 375047 286378 114073 873691 046308 241784 351660 877735 935869 718643 588907 708014 696426 223695 215890 396639 109787 527632 373010 198847 835500 305315 557803 536299 260384 > 4²⁵² [i]