Best Known (127, 127+102, s)-Nets in Base 4
(127, 127+102, 130)-Net over F4 — Constructive and digital
Digital (127, 229, 130)-net over F4, using
- t-expansion [i] based on digital (105, 229, 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
(127, 127+102, 233)-Net over F4 — Digital
Digital (127, 229, 233)-net over F4, using
(127, 127+102, 3300)-Net in Base 4 — Upper bound on s
There is no (127, 229, 3301)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 745015 456670 843501 912325 500960 717972 794265 164199 462233 220558 771367 460298 537178 695817 089073 056098 856626 406928 528743 927797 042199 835139 000912 > 4229 [i]