Best Known (248−91, 248, s)-Nets in Base 2
(248−91, 248, 112)-Net over F2 — Constructive and digital
Digital (157, 248, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 124, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
(248−91, 248, 135)-Net over F2 — Digital
Digital (157, 248, 135)-net over F2, using
(248−91, 248, 727)-Net in Base 2 — Upper bound on s
There is no (157, 248, 728)-net in base 2, because
- 1 times m-reduction [i] would yield (157, 247, 728)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 238 588920 120354 172355 063137 161663 395981 663130 213084 451590 249622 294897 679116 > 2247 [i]