Best Known (149, 149+89, s)-Nets in Base 2
(149, 149+89, 78)-Net over F2 — Constructive and digital
Digital (149, 238, 78)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (51, 95, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (51, 35)-sequence over F2, using
- digital (54, 143, 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
- digital (51, 95, 36)-net over F2, using
(149, 149+89, 86)-Net in Base 2 — Constructive
(149, 238, 86)-net in base 2, using
- trace code for nets [i] based on (30, 119, 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
(149, 149+89, 125)-Net over F2 — Digital
Digital (149, 238, 125)-net over F2, using
(149, 149+89, 658)-Net in Base 2 — Upper bound on s
There is no (149, 238, 659)-net in base 2, because
- 1 times m-reduction [i] would yield (149, 237, 659)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 223140 908983 124428 576179 902011 811235 591473 357620 785512 431042 222829 256240 > 2237 [i]