Best Known (61−28, 61, s)-Nets in Base 2
(61−28, 61, 25)-Net over F2 — Constructive and digital
Digital (33, 61, 25)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (8, 22, 11)-net over F2, using
- net from sequence [i] based on digital (8, 10)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 8 and N(F) ≥ 11, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (8, 10)-sequence over F2, using
- digital (11, 39, 14)-net over F2, using
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 11 and N(F) ≥ 14, using
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
- digital (8, 22, 11)-net over F2, using
(61−28, 61, 28)-Net over F2 — Digital
Digital (33, 61, 28)-net over F2, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
(61−28, 61, 99)-Net over F2 — Upper bound on s (digital)
There is no digital (33, 61, 100)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(261, 100, F2, 28) (dual of [100, 39, 29]-code), but
- adding a parity check bit [i] would yield linear OA(262, 101, F2, 29) (dual of [101, 39, 30]-code), but
- “Bro†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(262, 101, F2, 29) (dual of [101, 39, 30]-code), but
(61−28, 61, 100)-Net in Base 2 — Upper bound on s
There is no (33, 61, 101)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(261, 101, S2, 28), but
- the linear programming bound shows that M ≥ 6546 972925 691403 581923 536083 615744 / 2497 320966 828051 > 261 [i]