MinT - Best Known (244−58, 244, s)-Nets in Base 4

Best Known (244−58, 244, s)-Nets in Base 4

(244−58, 244, 1040)-Net over F₄ — Constructive and digital

Digital (186, 244, 1040)-net over F₄, using

trace code for nets [i] based on digital (3, 61, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(244−58, 244, 2809)-Net over F₄ — Digital

Digital (186, 244, 2809)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−58, 244, 452466)-Net in Base 4 — Upper bound on s

There is no (186, 244, 452467)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 799 202247 520718 168685 541808 010070 819487 862591 931667 886000 884657 419279 778395 747706 565897 772501 307181 844923 647561 399650 533214 955813 167327 038484 284592 > 4²⁴⁴ [i]