MinT - Best Known (222−67, 222, s)-Nets in Base 4

Best Known (222−67, 222, s)-Nets in Base 4

(222−67, 222, 531)-Net over F₄ — Constructive and digital

Digital (155, 222, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 74, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(222−67, 222, 885)-Net over F₄ — Digital

Digital (155, 222, 885)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−67, 222, 47202)-Net in Base 4 — Upper bound on s

There is no (155, 222, 47203)-net in base 4, because

1 times m-reduction [i] would yield (155, 221, 47203)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 363343 221282 409678 252575 519931 969105 841284 294513 511321 777917 790672 269384 225213 096732 234714 235515 499561 483324 701183 428969 594966 464630 > 4²²¹ [i]