Best Known (128, 128+119, s)-Nets in Base 4
(128, 128+119, 130)-Net over F4 — Constructive and digital
Digital (128, 247, 130)-net over F4, using
- t-expansion [i] based on digital (105, 247, 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
(128, 128+119, 195)-Net over F4 — Digital
Digital (128, 247, 195)-net over F4, using
(128, 128+119, 2414)-Net in Base 4 — Upper bound on s
There is no (128, 247, 2415)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 246, 2415)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12813 937835 661554 792255 349579 675287 250051 146531 353457 351750 018319 637708 550856 319275 500649 689673 295574 087128 538804 141910 662315 515907 154683 374358 005120 > 4246 [i]