MinT - Best Known (144, 144+71, s)-Nets in Base 2

Best Known (144, 144+71, s)-Nets in Base 2

(144, 144+71, 112)-Net over F₂ — Constructive and digital

Digital (144, 215, 112)-net over F₂, using

7 times m-reduction [i] based on digital (144, 222, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 111, 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]

(144, 144+71, 152)-Net over F₂ — Digital

Digital (144, 215, 152)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+71, 912)-Net in Base 2 — Upper bound on s

There is no (144, 215, 913)-net in base 2, because

1 times m-reduction [i] would yield (144, 214, 913)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26580 261344 416690 853494 998272 529860 954399 313263 365366 587170 326624 > 2²¹⁴ [i]