Best Known (246−94, 246, s)-Nets in Base 2
(246−94, 246, 78)-Net over F2 — Constructive and digital
Digital (152, 246, 78)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (51, 98, 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, 148, 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, 98, 36)-net over F2, using
(246−94, 246, 84)-Net in Base 2 — Constructive
(152, 246, 84)-net in base 2, using
- 4 times m-reduction [i] based on (152, 250, 84)-net in base 2, using
- trace code for nets [i] based on (27, 125, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [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
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- trace code for nets [i] based on (27, 125, 42)-net in base 4, using
(246−94, 246, 122)-Net over F2 — Digital
Digital (152, 246, 122)-net over F2, using
(246−94, 246, 624)-Net in Base 2 — Upper bound on s
There is no (152, 246, 625)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 117 532511 197148 496597 504896 197312 763148 884355 775941 690182 511783 839051 339776 > 2246 [i]