MinT - Best Known (158, 158+68, s)-Nets in Base 4

Best Known (158, 158+68, s)-Nets in Base 4

(158, 158+68, 531)-Net over F₄ — Constructive and digital

Digital (158, 226, 531)-net over F₄, using

4¹ times duplication [i] based on digital (157, 225, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 75, 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]

(158, 158+68, 910)-Net over F₄ — Digital

Digital (158, 226, 910)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+68, 45291)-Net in Base 4 — Upper bound on s

There is no (158, 226, 45292)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11634 782158 623683 138739 564750 475513 068665 632724 059890 329900 781510 480843 049009 602654 339617 630758 051054 281867 620209 423581 138432 303663 871609 > 4²²⁶ [i]