Best Known (154, 231, s)-Nets in Base 2
(154, 231, 112)-Net over F2 — Constructive and digital
Digital (154, 231, 112)-net over F2, using
- 11 times m-reduction [i] based on digital (154, 242, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 121, 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, 121, 56)-net over F4, using
(154, 231, 158)-Net over F2 — Digital
Digital (154, 231, 158)-net over F2, using
(154, 231, 942)-Net in Base 2 — Upper bound on s
There is no (154, 231, 943)-net in base 2, because
- 1 times m-reduction [i] would yield (154, 230, 943)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1777 248764 623903 598589 920573 105876 718010 136575 682434 012828 152672 753663 > 2230 [i]