Best Known (178, 254, s)-Nets in Base 2
(178, 254, 132)-Net over F2 — Constructive and digital
Digital (178, 254, 132)-net over F2, using
- 4 times m-reduction [i] based on digital (178, 258, 132)-net over F2, using
- trace code for nets [i] based on digital (49, 129, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second 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) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- trace code for nets [i] based on digital (49, 129, 66)-net over F4, using
(178, 254, 220)-Net over F2 — Digital
Digital (178, 254, 220)-net over F2, using
(178, 254, 1489)-Net in Base 2 — Upper bound on s
There is no (178, 254, 1490)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 29300 086875 499566 026861 924049 154594 046609 258545 736484 474574 178400 666054 741168 > 2254 [i]