Best Known (115, 115+103, s)-Nets in Base 4
(115, 115+103, 130)-Net over F4 — Constructive and digital
Digital (115, 218, 130)-net over F4, using
- t-expansion [i] based on digital (105, 218, 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
(115, 115+103, 185)-Net over F4 — Digital
Digital (115, 218, 185)-net over F4, using
(115, 115+103, 2370)-Net in Base 4 — Upper bound on s
There is no (115, 218, 2371)-net in base 4, because
- 1 times m-reduction [i] would yield (115, 217, 2371)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 44711 387437 266946 244412 828632 316163 909098 578062 341211 226290 833493 206363 125247 233222 507278 530841 279401 990290 579821 774628 542258 970704 > 4217 [i]