Best Known (36, 73, s)-Nets in Base 4
(36, 73, 56)-Net over F4 — Constructive and digital
Digital (36, 73, 56)-net over F4, using
- t-expansion [i] based on digital (33, 73, 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
(36, 73, 65)-Net over F4 — Digital
Digital (36, 73, 65)-net over F4, using
- t-expansion [i] based on digital (33, 73, 65)-net over F4, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 65, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
(36, 73, 630)-Net in Base 4 — Upper bound on s
There is no (36, 73, 631)-net in base 4, because
- 1 times m-reduction [i] would yield (36, 72, 631)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 22 827719 138278 557404 483620 450772 705494 861177 > 472 [i]