Best Known (129, 129+131, s)-Nets in Base 4
(129, 129+131, 130)-Net over F4 — Constructive and digital
Digital (129, 260, 130)-net over F4, using
- t-expansion [i] based on digital (105, 260, 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
(129, 129+131, 177)-Net over F4 — Digital
Digital (129, 260, 177)-net over F4, using
(129, 129+131, 2038)-Net in Base 4 — Upper bound on s
There is no (129, 260, 2039)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 259, 2039)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 861104 942134 763004 984117 900301 897919 051149 577044 469980 626682 598239 590941 699924 916323 812513 963484 778061 889012 318604 185293 764946 774842 146480 905363 128186 112630 > 4259 [i]