Best Known (81, 81+128, s)-Nets in Base 4
(81, 81+128, 104)-Net over F4 — Constructive and digital
Digital (81, 209, 104)-net over F4, using
- t-expansion [i] based on digital (73, 209, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(81, 81+128, 129)-Net over F4 — Digital
Digital (81, 209, 129)-net over F4, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 81 and N(F) ≥ 129, using
(81, 81+128, 709)-Net in Base 4 — Upper bound on s
There is no (81, 209, 710)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 722070 479064 942290 753574 730125 300471 502536 087380 174564 201558 329224 828065 859043 557378 570034 581605 256809 129881 472801 220158 180695 > 4209 [i]