Best Known (107, 107+105, s)-Nets in Base 4
(107, 107+105, 130)-Net over F4 — Constructive and digital
Digital (107, 212, 130)-net over F4, using
- t-expansion [i] based on digital (105, 212, 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
(107, 107+105, 156)-Net over F4 — Digital
Digital (107, 212, 156)-net over F4, using
(107, 107+105, 1827)-Net in Base 4 — Upper bound on s
There is no (107, 212, 1828)-net in base 4, because
- 1 times m-reduction [i] would yield (107, 211, 1828)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11 091918 447652 446794 321824 726458 935260 844472 394992 780038 155731 268088 207239 929100 196373 754862 262199 746109 656223 454350 841286 621760 > 4211 [i]