Best Known (125, 249, s)-Nets in Base 4
(125, 249, 130)-Net over F4 — Constructive and digital
Digital (125, 249, 130)-net over F4, using
- t-expansion [i] based on digital (105, 249, 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, 249, 177)-Net over F4 — Digital
Digital (125, 249, 177)-net over F4, using
(125, 249, 2037)-Net in Base 4 — Upper bound on s
There is no (125, 249, 2038)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 823870 420099 178229 141425 674030 950836 181257 691742 198501 246839 181487 706597 035294 014077 197940 523302 678942 930765 719485 684004 045980 359695 019153 912358 183840 > 4249 [i]