Best Known (171, 248, s)-Nets in Base 2
(171, 248, 112)-Net over F2 — Constructive and digital
Digital (171, 248, 112)-net over F2, using
- t-expansion [i] based on digital (163, 248, 112)-net over F2, using
- 12 times m-reduction [i] based on digital (163, 260, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 130, 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
- trace code for nets [i] based on digital (33, 130, 56)-net over F4, using
- 12 times m-reduction [i] based on digital (163, 260, 112)-net over F2, using
(171, 248, 198)-Net over F2 — Digital
Digital (171, 248, 198)-net over F2, using
(171, 248, 1304)-Net in Base 2 — Upper bound on s
There is no (171, 248, 1305)-net in base 2, because
- 1 times m-reduction [i] would yield (171, 247, 1305)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 229 826617 589112 876798 566627 875207 302127 076770 693341 598257 724300 396535 132896 > 2247 [i]