Best Known (88, 88+27, s)-Nets in Base 2
(88, 88+27, 144)-Net over F2 — Constructive and digital
Digital (88, 115, 144)-net over F2, using
- 21 times duplication [i] based on digital (87, 114, 144)-net over F2, using
- trace code for nets [i] based on digital (11, 38, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- trace code for nets [i] based on digital (11, 38, 48)-net over F8, using
(88, 88+27, 212)-Net over F2 — Digital
Digital (88, 115, 212)-net over F2, using
(88, 88+27, 2453)-Net in Base 2 — Upper bound on s
There is no (88, 115, 2454)-net in base 2, because
- 1 times m-reduction [i] would yield (88, 114, 2454)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 20772 240900 619077 559262 415324 498102 > 2114 [i]