Best Known (129, 129+103, s)-Nets in Base 4
(129, 129+103, 130)-Net over F4 — Constructive and digital
Digital (129, 232, 130)-net over F4, using
- t-expansion [i] based on digital (105, 232, 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
(129, 129+103, 238)-Net over F4 — Digital
Digital (129, 232, 238)-net over F4, using
(129, 129+103, 3487)-Net in Base 4 — Upper bound on s
There is no (129, 232, 3488)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 231, 3488)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11 963457 216835 654783 767677 110500 157356 107542 319482 952752 709460 890170 032104 386161 754600 264031 145494 854855 991214 919818 488778 290141 143128 518740 > 4231 [i]