Best Known (246−84, 246, s)-Nets in Base 2
(246−84, 246, 112)-Net over F2 — Constructive and digital
Digital (162, 246, 112)-net over F2, using
- 12 times m-reduction [i] based on digital (162, 258, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 129, 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, 129, 56)-net over F4, using
(246−84, 246, 158)-Net over F2 — Digital
Digital (162, 246, 158)-net over F2, using
(246−84, 246, 896)-Net in Base 2 — Upper bound on s
There is no (162, 246, 897)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 115 845083 492830 281638 128902 866958 090023 787961 321707 993800 043147 995533 110656 > 2246 [i]