Best Known (125, 125+110, s)-Nets in Base 4
(125, 125+110, 130)-Net over F4 — Constructive and digital
Digital (125, 235, 130)-net over F4, using
- t-expansion [i] based on digital (105, 235, 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+110, 204)-Net over F4 — Digital
Digital (125, 235, 204)-net over F4, using
(125, 125+110, 2612)-Net in Base 4 — Upper bound on s
There is no (125, 235, 2613)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3082 296848 720472 381811 613320 072704 256149 155090 815988 698693 798579 608640 021364 470772 764978 286308 430649 313335 113346 263265 376887 251528 353551 183040 > 4235 [i]