MinT - Best Known (198−66, 198, s)-Nets in Base 2

Best Known (198−66, 198, s)-Nets in Base 2

(198−66, 198, 112)-Net over F₂ — Constructive and digital

Digital (132, 198, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 99, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(198−66, 198, 139)-Net over F₂ — Digital

Digital (132, 198, 139)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−66, 198, 794)-Net in Base 2 — Upper bound on s

There is no (132, 198, 795)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 406581 133436 095135 159287 542496 294981 287803 280791 667185 490080 > 2¹⁹⁸ [i]