Best Known (55, 55+87, s)-Nets in Base 2
(55, 55+87, 42)-Net over F2 — Constructive and digital
Digital (55, 142, 42)-net over F2, using
- t-expansion [i] based on digital (54, 142, 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, 55+87, 109)-Net in Base 2 — Upper bound on s
There is no (55, 142, 110)-net in base 2, because
- 1 times m-reduction [i] would yield (55, 141, 110)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3 306374 811469 989684 124603 977571 376689 540530 > 2141 [i]