Best Known (74, 74+127, s)-Nets in Base 4
(74, 74+127, 104)-Net over F4 — Constructive and digital
Digital (74, 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
(74, 74+127, 112)-Net over F4 — Digital
Digital (74, 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
(74, 74+127, 609)-Net in Base 4 — Upper bound on s
There is no (74, 201, 610)-net in base 4, because
- 1 times m-reduction [i] would yield (74, 200, 610)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 590102 459107 264349 100379 422604 516688 069740 451906 465925 199487 220299 566238 091133 517006 817963 016368 810185 005073 406620 836640 > 4200 [i]