Best Known (55, 111, s)-Nets in Base 2
(55, 111, 42)-Net over F2 — Constructive and digital
Digital (55, 111, 42)-net over F2, using
- t-expansion [i] based on digital (54, 111, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
(55, 111, 119)-Net over F2 — Upper bound on s (digital)
There is no digital (55, 111, 120)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2111, 120, F2, 56) (dual of [120, 9, 57]-code), but
- residual code [i] would yield linear OA(255, 63, F2, 28) (dual of [63, 8, 29]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(255, 63, F2, 28) (dual of [63, 8, 29]-code), but
(55, 111, 121)-Net in Base 2 — Upper bound on s
There is no (55, 111, 122)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2111, 122, S2, 56), but
- the linear programming bound shows that M ≥ 53 252196 581133 192158 208770 352481 304576 / 17255 > 2111 [i]