Best Known (156, 156+66, s)-Nets in Base 2
(156, 156+66, 112)-Net over F2 — Constructive and digital
Digital (156, 222, 112)-net over F2, using
- 24 times m-reduction [i] based on digital (156, 246, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 123, 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, 123, 56)-net over F4, using
(156, 156+66, 199)-Net over F2 — Digital
Digital (156, 222, 199)-net over F2, using
(156, 156+66, 1346)-Net in Base 2 — Upper bound on s
There is no (156, 222, 1347)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6 832724 155079 064553 003428 260129 286937 630873 119620 202575 046239 695800 > 2222 [i]