Best Known (124, 124+98, s)-Nets in Base 4
(124, 124+98, 130)-Net over F4 — Constructive and digital
Digital (124, 222, 130)-net over F4, using
- t-expansion [i] based on digital (105, 222, 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
(124, 124+98, 233)-Net over F4 — Digital
Digital (124, 222, 233)-net over F4, using
(124, 124+98, 3363)-Net in Base 4 — Upper bound on s
There is no (124, 222, 3364)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 46 054519 157640 157548 491822 280740 794445 208732 803528 524603 048457 759406 829464 345603 561987 957944 665740 050831 660331 816082 829308 900821 568144 > 4222 [i]