Best Known (82, 82+123, s)-Nets in Base 4
(82, 82+123, 104)-Net over F4 — Constructive and digital
Digital (82, 205, 104)-net over F4, using
- t-expansion [i] based on digital (73, 205, 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+123, 129)-Net over F4 — Digital
Digital (82, 205, 129)-net over F4, using
- t-expansion [i] based on digital (81, 205, 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+123, 760)-Net in Base 4 — Upper bound on s
There is no (82, 205, 761)-net in base 4, because
- 1 times m-reduction [i] would yield (82, 204, 761)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 664 123144 707659 416715 008744 615401 403507 192844 042131 355110 903734 088321 463885 129924 422923 081694 864936 948323 574954 980537 108352 > 4204 [i]