MinT - Best Known (238−72, 238, s)-Nets in Base 4

Best Known (238−72, 238, s)-Nets in Base 4

(238−72, 238, 531)-Net over F₄ — Constructive and digital

Digital (166, 238, 531)-net over F₄, using

4¹ times duplication [i] based on digital (165, 237, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 79, 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]

(238−72, 238, 930)-Net over F₄ — Digital

Digital (166, 238, 930)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−72, 238, 45458)-Net in Base 4 — Upper bound on s

There is no (166, 238, 45459)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195112 761632 252444 736074 941344 401974 042441 835541 578136 806175 305937 860707 732919 203503 032493 613412 111448 707225 392649 407361 441124 934453 799299 122640 > 4²³⁸ [i]