Best Known (135, 135+69, s)-Nets in Base 2
(135, 135+69, 112)-Net over F2 — Constructive and digital
Digital (135, 204, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 102, 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
(135, 135+69, 138)-Net over F2 — Digital
Digital (135, 204, 138)-net over F2, using
(135, 135+69, 799)-Net in Base 2 — Upper bound on s
There is no (135, 204, 800)-net in base 2, because
- 1 times m-reduction [i] would yield (135, 203, 800)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 13 050770 769238 934901 176913 452856 052404 093994 417417 164528 941208 > 2203 [i]