MinT - Best Known (229−81, 229, s)-Nets in Base 2

Best Known (229−81, 229, s)-Nets in Base 2

(229−81, 229, 112)-Net over F₂ — Constructive and digital

Digital (148, 229, 112)-net over F₂, using

1 times m-reduction [i] based on digital (148, 230, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 115, 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]

(229−81, 229, 137)-Net over F₂ — Digital

Digital (148, 229, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−81, 229, 762)-Net in Base 2 — Upper bound on s

There is no (148, 229, 763)-net in base 2, because

1 times m-reduction [i] would yield (148, 228, 763)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 450 412777 458257 997419 123735 339315 272369 418135 332764 505567 148531 693511 > 2²²⁸ [i]