MinT - Best Known (158−102, 158, s)-Nets in Base 4

Best Known (158−102, 158, s)-Nets in Base 4

(158−102, 158, 66)-Net over F₄ — Constructive and digital

Digital (56, 158, 66)-net over F₄, using

t-expansion [i] based on digital (49, 158, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(158−102, 158, 91)-Net over F₄ — Digital

Digital (56, 158, 91)-net over F₄, using

t-expansion [i] based on digital (50, 158, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(158−102, 158, 444)-Net in Base 4 — Upper bound on s

There is no (56, 158, 445)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 139949 764985 431659 777685 284248 136222 952869 213370 751486 769634 467940 650836 932563 639330 874728 384388 > 4¹⁵⁸ [i]