Best Known (125, 125+104, s)-Nets in Base 4
(125, 125+104, 130)-Net over F4 — Constructive and digital
Digital (125, 229, 130)-net over F4, using
- t-expansion [i] based on digital (105, 229, 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
(125, 125+104, 219)-Net over F4 — Digital
Digital (125, 229, 219)-net over F4, using
(125, 125+104, 2978)-Net in Base 4 — Upper bound on s
There is no (125, 229, 2979)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 751623 296949 481120 752143 139743 724979 348000 693859 903879 218564 932970 132788 453951 265474 246766 140769 112234 515648 322623 169692 343029 742960 795040 > 4229 [i]