Best Known (91, 91+41, s)-Nets in Base 2
(91, 91+41, 72)-Net over F2 — Constructive and digital
Digital (91, 132, 72)-net over F2, using
- trace code for nets [i] based on digital (3, 44, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
(91, 91+41, 117)-Net over F2 — Digital
Digital (91, 132, 117)-net over F2, using
(91, 91+41, 749)-Net in Base 2 — Upper bound on s
There is no (91, 132, 750)-net in base 2, because
- 1 times m-reduction [i] would yield (91, 131, 750)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2783 837064 053980 457936 011136 080735 902226 > 2131 [i]