Best Known (115, 115+107, s)-Nets in Base 4
(115, 115+107, 130)-Net over F4 — Constructive and digital
Digital (115, 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
(115, 115+107, 177)-Net over F4 — Digital
Digital (115, 222, 177)-net over F4, using
(115, 115+107, 2180)-Net in Base 4 — Upper bound on s
There is no (115, 222, 2181)-net in base 4, because
- 1 times m-reduction [i] would yield (115, 221, 2181)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11 433700 624070 394053 205004 984741 021466 757695 015601 568483 265032 604781 782747 415574 843646 586206 033820 595158 032445 583894 577616 135764 455072 > 4221 [i]