Best Known (144, 144+78, s)-Nets in Base 2
(144, 144+78, 112)-Net over F2 — Constructive and digital
Digital (144, 222, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 111, 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
(144, 144+78, 135)-Net over F2 — Digital
Digital (144, 222, 135)-net over F2, using
(144, 144+78, 739)-Net in Base 2 — Upper bound on s
There is no (144, 222, 740)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6 745180 851927 208932 617264 882367 538688 388878 391908 626547 354461 651488 > 2222 [i]