Best Known (88, 88+37, s)-Nets in Base 2
(88, 88+37, 75)-Net over F2 — Constructive and digital
Digital (88, 125, 75)-net over F2, using
- 1 times m-reduction [i] based on digital (88, 126, 75)-net over F2, using
- trace code for nets [i] based on digital (4, 42, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- trace code for nets [i] based on digital (4, 42, 25)-net over F8, using
(88, 88+37, 126)-Net over F2 — Digital
Digital (88, 125, 126)-net over F2, using
(88, 88+37, 868)-Net in Base 2 — Upper bound on s
There is no (88, 125, 869)-net in base 2, because
- 1 times m-reduction [i] would yield (88, 124, 869)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 21 270392 437422 287356 679376 221521 887124 > 2124 [i]