MinT - Best Known (221−62, 221, s)-Nets in Base 4

Best Known (221−62, 221, s)-Nets in Base 4

(221−62, 221, 531)-Net over F₄ — Constructive and digital

Digital (159, 221, 531)-net over F₄, using

7 times m-reduction [i] based on digital (159, 228, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 76, 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]

(221−62, 221, 1203)-Net over F₄ — Digital

Digital (159, 221, 1203)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−62, 221, 81073)-Net in Base 4 — Upper bound on s

There is no (159, 221, 81074)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 357230 283442 634114 754190 668093 650866 253167 293773 800780 711835 589030 881116 985551 692235 686056 286864 804396 046822 711864 648705 157182 364240 > 4²²¹ [i]