MinT - Best Known (234−81, 234, s)-Nets in Base 2

Best Known (234−81, 234, s)-Nets in Base 2

(234−81, 234, 112)-Net over F₂ — Constructive and digital

Digital (153, 234, 112)-net over F₂, using

6 times m-reduction [i] based on digital (153, 240, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 120, 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]

(234−81, 234, 146)-Net over F₂ — Digital

Digital (153, 234, 146)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−81, 234, 836)-Net in Base 2 — Upper bound on s

There is no (153, 234, 837)-net in base 2, because

1 times m-reduction [i] would yield (153, 233, 837)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14336 745333 858365 140261 473340 329271 425166 611261 088378 202028 929258 798840 > 2²³³ [i]