MinT - Best Known (43, 87, s)-Nets in Base 2

Best Known (43, 87, s)-Nets in Base 2

(43, 87, 33)-Net over F₂ — Constructive and digital

Digital (43, 87, 33)-net over F₂, using

t-expansion [i] based on digital (39, 87, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(43, 87, 34)-Net over F₂ — Digital

Digital (43, 87, 34)-net over F₂, using

net from sequence [i] based on digital (43, 33)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 43 and N(F) ≥ 34, using
  - a curve from the manYPoints database [i]

(43, 87, 95)-Net over F₂ — Upper bound on s (digital)

There is no digital (43, 87, 96)-net over F₂, because

extracting embedded orthogonal array [i] would yield linear OA(2⁸⁷, 96, F₂, 44) (dual of [96, 9, 45]-code), but
- â€œJaâ€ bound on codes from Brouwerâ€™s database [i]

(43, 87, 97)-Net in Base 2 — Upper bound on s

There is no (43, 87, 98)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁸⁷, 98, S₂, 44), but
- the linear programming bound shows that MÂ â‰¥ 903696 228678 327600 676360 683520 / 4669 > 2⁸⁷ [i]