Best Known (232−108, 232, s)-Nets in Base 4
(232−108, 232, 130)-Net over F4 — Constructive and digital
Digital (124, 232, 130)-net over F4, using
- t-expansion [i] based on digital (105, 232, 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
(232−108, 232, 205)-Net over F4 — Digital
Digital (124, 232, 205)-net over F4, using
(232−108, 232, 2653)-Net in Base 4 — Upper bound on s
There is no (124, 232, 2654)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 47 799384 739641 508623 215592 078429 620290 998111 410248 715762 141369 929013 400153 110212 721084 575258 700279 878229 818878 521031 115061 630284 770682 801480 > 4232 [i]