Best Known (128, 249, s)-Nets in Base 4
(128, 249, 130)-Net over F4 — Constructive and digital
Digital (128, 249, 130)-net over F4, using
- t-expansion [i] based on digital (105, 249, 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, 249, 191)-Net over F4 — Digital
Digital (128, 249, 191)-net over F4, using
(128, 249, 2331)-Net in Base 4 — Upper bound on s
There is no (128, 249, 2332)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 248, 2332)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 206005 685443 574017 678816 327358 544172 174961 796564 360032 408672 074908 856199 984278 309725 747102 961233 421628 247540 892008 912499 273852 969257 604060 600233 123520 > 4248 [i]