MinT - Best Known (215−85, 215, s)-Nets in Base 2

Best Known (215−85, 215, s)-Nets in Base 2

(215−85, 215, 68)-Net over F₂ — Constructive and digital

Digital (130, 215, 68)-net over F₂, using

3 times m-reduction [i] based on digital (130, 218, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 109, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(215−85, 215, 101)-Net over F₂ — Digital

Digital (130, 215, 101)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−85, 215, 504)-Net in Base 2 — Upper bound on s

There is no (130, 215, 505)-net in base 2, because

1 times m-reduction [i] would yield (130, 214, 505)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26464 154424 881545 389620 051453 994958 097115 763495 421201 674587 407396 > 2²¹⁴ [i]