Best Known (119, 119+103, s)-Nets in Base 4
(119, 119+103, 130)-Net over F4 — Constructive and digital
Digital (119, 222, 130)-net over F4, using
- t-expansion [i] based on digital (105, 222, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(119, 119+103, 199)-Net over F4 — Digital
Digital (119, 222, 199)-net over F4, using
(119, 119+103, 2647)-Net in Base 4 — Upper bound on s
There is no (119, 222, 2648)-net in base 4, because
- 1 times m-reduction [i] would yield (119, 221, 2648)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11 424997 717824 828559 101543 622515 857036 437981 618718 692642 479515 530202 554564 672393 035407 542234 633744 973986 962017 679603 383298 224953 247170 > 4221 [i]