Best Known (128, 128+97, s)-Nets in Base 4
(128, 128+97, 130)-Net over F4 — Constructive and digital
Digital (128, 225, 130)-net over F4, using
- t-expansion [i] based on digital (105, 225, 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+97, 255)-Net over F4 — Digital
Digital (128, 225, 255)-net over F4, using
(128, 128+97, 3990)-Net in Base 4 — Upper bound on s
There is no (128, 225, 3991)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 224, 3991)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 731 774704 629175 492419 445647 947387 772556 001000 976595 781184 190290 113063 874889 221462 280495 104370 410422 641417 212713 449263 873546 564586 872076 > 4224 [i]