Best Known (73, 138, s)-Nets in Base 4
(73, 138, 104)-Net over F4 — Constructive and digital
Digital (73, 138, 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
(73, 138, 126)-Net over F4 — Digital
Digital (73, 138, 126)-net over F4, using
(73, 138, 1585)-Net in Base 4 — Upper bound on s
There is no (73, 138, 1586)-net in base 4, because
- 1 times m-reduction [i] would yield (73, 137, 1586)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 30439 081832 951802 636440 139709 760772 131539 133176 849032 095664 627058 178846 431225 285375 > 4137 [i]