Best Known (106, 106+145, s)-Nets in Base 2
(106, 106+145, 56)-Net over F2 — Constructive and digital
Digital (106, 251, 56)-net over F2, using
- t-expansion [i] based on digital (105, 251, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 7 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (105, 55)-sequence over F2, using
(106, 106+145, 65)-Net over F2 — Digital
Digital (106, 251, 65)-net over F2, using
- t-expansion [i] based on digital (95, 251, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(106, 106+145, 213)-Net in Base 2 — Upper bound on s
There is no (106, 251, 214)-net in base 2, because
- 1 times m-reduction [i] would yield (106, 250, 214)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1921 996108 585485 847559 885573 873202 025906 773928 593303 614315 536666 195214 957894 > 2250 [i]