Best Known (134, 233, s)-Nets in Base 2
(134, 233, 67)-Net over F2 — Constructive and digital
Digital (134, 233, 67)-net over F2, using
- 1 times m-reduction [i] based on digital (134, 234, 67)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 89, 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 (45, 145, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-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 1 place 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 (45, 33)-sequence over F2, using
- digital (39, 89, 33)-net over F2, using
- (u, u+v)-construction [i] based on
(134, 233, 92)-Net over F2 — Digital
Digital (134, 233, 92)-net over F2, using
(134, 233, 440)-Net in Base 2 — Upper bound on s
There is no (134, 233, 441)-net in base 2, because
- 1 times m-reduction [i] would yield (134, 232, 441)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 7387 041586 911463 322763 278852 051479 081690 635204 973424 344558 608565 991478 > 2232 [i]