Best Known (126, 126+122, s)-Nets in Base 4
(126, 126+122, 130)-Net over F4 — Constructive and digital
Digital (126, 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
(126, 126+122, 183)-Net over F4 — Digital
Digital (126, 248, 183)-net over F4, using
(126, 126+122, 2152)-Net in Base 4 — Upper bound on s
There is no (126, 248, 2153)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 209683 002019 674746 855324 490835 430299 891755 300886 515624 763194 416231 113228 661366 288494 483459 942591 167662 211830 480509 473162 106323 523398 684257 713965 001600 > 4248 [i]