Best Known (85, 85+57, s)-Nets in Base 2
(85, 85+57, 60)-Net over F2 — Constructive and digital
Digital (85, 142, 60)-net over F2, using
- 2 times m-reduction [i] based on digital (85, 144, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 72, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 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) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- trace code for nets [i] based on digital (13, 72, 30)-net over F4, using
(85, 85+57, 69)-Net over F2 — Digital
Digital (85, 142, 69)-net over F2, using
(85, 85+57, 331)-Net in Base 2 — Upper bound on s
There is no (85, 142, 332)-net in base 2, because
- 1 times m-reduction [i] would yield (85, 141, 332)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 984614 495190 709398 348527 933218 172650 992400 > 2141 [i]