Best Known (238−108, 238, s)-Nets in Base 2
(238−108, 238, 63)-Net over F2 — Constructive and digital
Digital (130, 238, 63)-net over F2, using
- 2 times m-reduction [i] based on digital (130, 240, 63)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 76, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- digital (54, 164, 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 (21, 76, 21)-net over F2, using
- (u, u+v)-construction [i] based on
(238−108, 238, 81)-Net over F2 — Digital
Digital (130, 238, 81)-net over F2, using
- t-expansion [i] based on digital (126, 238, 81)-net over F2, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 126 and N(F) ≥ 81, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
(238−108, 238, 286)-Net in Base 2 — Upper bound on s
There is no (130, 238, 287)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2238, 287, S2, 108), but
- the linear programming bound shows that M ≥ 2 133520 632200 595168 112459 587583 515002 010526 895398 363193 388655 973626 286863 730797 742512 930816 / 4 628313 007677 734375 > 2238 [i]