Best Known (163, 163+97, s)-Nets in Base 2
(163, 163+97, 112)-Net over F2 — Constructive and digital
Digital (163, 260, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 130, 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
(163, 163+97, 135)-Net over F2 — Digital
Digital (163, 260, 135)-net over F2, using
(163, 163+97, 720)-Net in Base 2 — Upper bound on s
There is no (163, 260, 721)-net in base 2, because
- 1 times m-reduction [i] would yield (163, 259, 721)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 962914 008260 184675 264041 046191 917115 530716 197619 798291 449440 673503 955445 249830 > 2259 [i]