Best Known (107, 107+77, s)-Nets in Base 4
(107, 107+77, 130)-Net over F4 — Constructive and digital
Digital (107, 184, 130)-net over F4, using
- t-expansion [i] based on digital (105, 184, 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+77, 235)-Net over F4 — Digital
Digital (107, 184, 235)-net over F4, using
(107, 107+77, 3941)-Net in Base 4 — Upper bound on s
There is no (107, 184, 3942)-net in base 4, because
- 1 times m-reduction [i] would yield (107, 183, 3942)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 150 972239 315334 314583 162958 487018 804672 516009 353830 982229 375173 491566 821112 576432 187495 249078 869171 689334 616040 > 4183 [i]