MinT - Best Known (154, 154+83, s)-Nets in Base 2

Best Known (154, 154+83, s)-Nets in Base 2

(154, 154+83, 112)-Net over F₂ — Constructive and digital

Digital (154, 237, 112)-net over F₂, using

5 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]

(154, 154+83, 144)-Net over F₂ — Digital

Digital (154, 237, 144)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+83, 813)-Net in Base 2 — Upper bound on s

There is no (154, 237, 814)-net in base 2, because

1 times m-reduction [i] would yield (154, 236, 814)-net in base 2, but
- 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]