MinT - Best Known (154, 154+75, s)-Nets in Base 2

Best Known (154, 154+75, s)-Nets in Base 2

(154, 154+75, 112)-Net over F₂ — Constructive and digital

Digital (154, 229, 112)-net over F₂, using

13 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+75, 163)-Net over F₂ — Digital

Digital (154, 229, 163)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+75, 995)-Net in Base 2 — Upper bound on s

There is no (154, 229, 996)-net in base 2, because

1 times m-reduction [i] would yield (154, 228, 996)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 437 456735 392247 576786 683230 626842 666674 666326 916275 011721 099335 530824 > 2²²⁸ [i]