Best Known (138, 138+120, s)-Nets in Base 2
(138, 138+120, 66)-Net over F2 — Constructive and digital
Digital (138, 258, 66)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 99, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- digital (39, 159, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2 (see above)
- digital (39, 99, 33)-net over F2, using
(138, 138+120, 81)-Net over F2 — Digital
Digital (138, 258, 81)-net over F2, using
- t-expansion [i] based on digital (126, 258, 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
(138, 138+120, 374)-Net in Base 2 — Upper bound on s
There is no (138, 258, 375)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 488766 158929 515371 612565 721061 409461 875551 461384 364055 748230 860693 638573 981176 > 2258 [i]