MinT - Best Known (257−72, 257, s)-Nets in Base 4

Best Known (257−72, 257, s)-Nets in Base 4

(257−72, 257, 531)-Net over F₄ — Constructive and digital

Digital (185, 257, 531)-net over F₄, using

t-expansion [i] based on digital (179, 257, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 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]

(257−72, 257, 1376)-Net over F₄ — Digital

Digital (185, 257, 1376)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−72, 257, 94519)-Net in Base 4 — Upper bound on s

There is no (185, 257, 94520)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53649 039634 011137 348542 571882 724463 773035 019350 297569 382050 243262 388320 678606 774752 862731 419765 170567 834860 705837 954136 371821 428317 775499 654360 395825 527585 > 4²⁵⁷ [i]