Best Known (74, 137, s)-Nets in Base 4
(74, 137, 104)-Net over F4 — Constructive and digital
Digital (74, 137, 104)-net over F4, using
- t-expansion [i] based on digital (73, 137, 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
(74, 137, 135)-Net over F4 — Digital
Digital (74, 137, 135)-net over F4, using
(74, 137, 1787)-Net in Base 4 — Upper bound on s
There is no (74, 137, 1788)-net in base 4, because
- 1 times m-reduction [i] would yield (74, 136, 1788)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7718 652306 175780 913431 786112 249913 355956 169705 532177 695832 076330 493577 015228 226760 > 4136 [i]