MinT - Best Known (236−82, 236, s)-Nets in Base 2

Best Known (236−82, 236, s)-Nets in Base 2

(236−82, 236, 112)-Net over F₂ — Constructive and digital

Digital (154, 236, 112)-net over F₂, using

6 times m-reduction [i] based on digital (154, 242, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 121, 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]

(236−82, 236, 146)-Net over F₂ — Digital

Digital (154, 236, 146)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−82, 236, 813)-Net in Base 2 — Upper bound on s

There is no (154, 236, 814)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 114709 541321 162386 714606 553511 380939 580145 333372 009660 180542 363182 256825 > 2²³⁶ [i]