MinT - Best Known (156, 156+90, s)-Nets in Base 2

Best Known (156, 156+90, s)-Nets in Base 2

(156, 156+90, 112)-Net over F₂ — Constructive and digital

Digital (156, 246, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 123, 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]

(156, 156+90, 135)-Net over F₂ — Digital

Digital (156, 246, 135)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+90, 714)-Net in Base 2 — Upper bound on s

There is no (156, 246, 715)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 113 090377 727375 500362 077499 985642 248821 950814 473170 639215 355090 636328 924640 > 2²⁴⁶ [i]