Best Known (115, 115+51, s)-Nets in Base 2
(115, 115+51, 78)-Net over F2 — Constructive and digital
Digital (115, 166, 78)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (9, 34, 12)-net over F2, using
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 9 and N(F) ≥ 12, using
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
- digital (81, 132, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 66, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- trace code for nets [i] based on digital (15, 66, 33)-net over F4, using
- digital (9, 34, 12)-net over F2, using
(115, 115+51, 86)-Net in Base 2 — Constructive
(115, 166, 86)-net in base 2, using
- 4 times m-reduction [i] based on (115, 170, 86)-net in base 2, using
- trace code for nets [i] based on (30, 85, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- trace code for nets [i] based on (30, 85, 43)-net in base 4, using
(115, 115+51, 145)-Net over F2 — Digital
Digital (115, 166, 145)-net over F2, using
(115, 115+51, 950)-Net in Base 2 — Upper bound on s
There is no (115, 166, 951)-net in base 2, because
- 1 times m-reduction [i] would yield (115, 165, 951)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 46 930870 463101 168525 143147 163557 420299 015225 109920 > 2165 [i]