Best Known (80, 80+121, s)-Nets in Base 4
(80, 80+121, 104)-Net over F4 — Constructive and digital
Digital (80, 201, 104)-net over F4, using
- t-expansion [i] based on digital (73, 201, 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
(80, 80+121, 112)-Net over F4 — Digital
Digital (80, 201, 112)-net over F4, using
- t-expansion [i] based on digital (73, 201, 112)-net over F4, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 112, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
(80, 80+121, 737)-Net in Base 4 — Upper bound on s
There is no (80, 201, 738)-net in base 4, because
- 1 times m-reduction [i] would yield (80, 200, 738)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 779540 463555 766377 746943 244302 667950 401324 534187 590812 310042 414429 246008 586880 148975 828799 667950 163135 987830 493884 347568 > 4200 [i]