Best Known (82, 82+105, s)-Nets in Base 4
(82, 82+105, 104)-Net over F4 — Constructive and digital
Digital (82, 187, 104)-net over F4, using
- t-expansion [i] based on digital (73, 187, 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
(82, 82+105, 129)-Net over F4 — Digital
Digital (82, 187, 129)-net over F4, using
- t-expansion [i] based on digital (81, 187, 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
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
(82, 82+105, 917)-Net in Base 4 — Upper bound on s
There is no (82, 187, 918)-net in base 4, because
- 1 times m-reduction [i] would yield (82, 186, 918)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 9650 861357 610670 442168 001693 791313 967976 303506 226998 423443 552011 531502 645357 848663 963623 777333 953592 651207 681900 > 4186 [i]