Best Known (129, 129+119, s)-Nets in Base 4
(129, 129+119, 130)-Net over F4 — Constructive and digital
Digital (129, 248, 130)-net over F4, using
- t-expansion [i] based on digital (105, 248, 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+119, 198)-Net over F4 — Digital
Digital (129, 248, 198)-net over F4, using
(129, 129+119, 2473)-Net in Base 4 — Upper bound on s
There is no (129, 248, 2474)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 247, 2474)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 51790 962126 807865 894745 434374 224394 173164 533688 873599 388359 074766 899614 424110 950642 365173 036301 831188 002813 356877 543150 653606 410260 058677 442057 190080 > 4247 [i]