Best Known (189, 238, s)-Nets in Base 2
(189, 238, 260)-Net over F2 — Constructive and digital
Digital (189, 238, 260)-net over F2, using
- 6 times m-reduction [i] based on digital (189, 244, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 61, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 61, 65)-net over F16, using
(189, 238, 549)-Net over F2 — Digital
Digital (189, 238, 549)-net over F2, using
(189, 238, 9169)-Net in Base 2 — Upper bound on s
There is no (189, 238, 9170)-net in base 2, because
- 1 times m-reduction [i] would yield (189, 237, 9170)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 220983 997115 501250 909760 652710 792220 088560 595517 712540 379834 696416 423192 > 2237 [i]