Best Known (125, 125+87, s)-Nets in Base 4
(125, 125+87, 130)-Net over F4 — Constructive and digital
Digital (125, 212, 130)-net over F4, using
- t-expansion [i] based on digital (105, 212, 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+87, 283)-Net over F4 — Digital
Digital (125, 212, 283)-net over F4, using
(125, 125+87, 5030)-Net in Base 4 — Upper bound on s
There is no (125, 212, 5031)-net in base 4, because
- 1 times m-reduction [i] would yield (125, 211, 5031)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10 878080 171193 358487 591632 777384 566956 179602 009038 607470 457664 221337 974206 947673 386091 735705 269433 459133 397827 820481 066026 297984 > 4211 [i]