Best Known (128, 128+115, s)-Nets in Base 4
(128, 128+115, 130)-Net over F4 — Constructive and digital
Digital (128, 243, 130)-net over F4, using
- t-expansion [i] based on digital (105, 243, 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+115, 203)-Net over F4 — Digital
Digital (128, 243, 203)-net over F4, using
(128, 128+115, 2601)-Net in Base 4 — Upper bound on s
There is no (128, 243, 2602)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 242, 2602)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 50 221264 938328 327674 854860 829566 081899 794236 554933 741650 966722 960655 871688 879092 744642 566978 111059 321045 694330 251523 390495 409846 491125 205674 544800 > 4242 [i]