MinT - Best Known (213−61, 213, s)-Nets in Base 4

Best Known (213−61, 213, s)-Nets in Base 4

(213−61, 213, 531)-Net over F₄ — Constructive and digital

Digital (152, 213, 531)-net over F₄, using

t-expansion [i] based on digital (151, 213, 531)-net over F₄, using
- 3 times m-reduction [i] based on digital (151, 216, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 72, 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]

(213−61, 213, 1065)-Net over F₄ — Digital

Digital (152, 213, 1065)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−61, 213, 72123)-Net in Base 4 — Upper bound on s

There is no (152, 213, 72124)-net in base 4, because

1 times m-reduction [i] would yield (152, 212, 72124)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 330747 331840 683396 271625 307592 421715 772926 389632 303913 688851 007158 352133 016119 689576 638914 929283 270285 170958 359611 767464 365016 > 4²¹² [i]