Best Known (127−33, 127, s)-Nets in Base 2
(127−33, 127, 135)-Net over F2 — Constructive and digital
Digital (94, 127, 135)-net over F2, using
- 21 times duplication [i] based on digital (93, 126, 135)-net over F2, using
- trace code for nets [i] based on digital (9, 42, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- trace code for nets [i] based on digital (9, 42, 45)-net over F8, using
(127−33, 127, 176)-Net over F2 — Digital
Digital (94, 127, 176)-net over F2, using
(127−33, 127, 1573)-Net in Base 2 — Upper bound on s
There is no (94, 127, 1574)-net in base 2, because
- 1 times m-reduction [i] would yield (94, 126, 1574)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 85 853383 093621 500890 946793 312296 150510 > 2126 [i]