MinT - Best Known (216−50, 216, s)-Nets in Base 4

Best Known (216−50, 216, s)-Nets in Base 4

(216−50, 216, 1044)-Net over F₄ — Constructive and digital

Digital (166, 216, 1044)-net over F₄, using

trace code for nets [i] based on digital (4, 54, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(216−50, 216, 2896)-Net over F₄ — Digital

Digital (166, 216, 2896)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−50, 216, 539866)-Net in Base 4 — Upper bound on s

There is no (166, 216, 539867)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11090 832362 039866 255490 138038 548156 612799 573239 452400 249830 021903 237465 498172 405210 432510 784701 379868 266306 765505 378184 284510 829946 > 4²¹⁶ [i]