Best Known (125, 125+121, s)-Nets in Base 4
(125, 125+121, 130)-Net over F4 — Constructive and digital
Digital (125, 246, 130)-net over F4, using
- t-expansion [i] based on digital (105, 246, 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+121, 182)-Net over F4 — Digital
Digital (125, 246, 182)-net over F4, using
(125, 125+121, 2172)-Net in Base 4 — Upper bound on s
There is no (125, 246, 2173)-net in base 4, because
- 1 times m-reduction [i] would yield (125, 245, 2173)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3256 290335 114731 030330 142380 644183 214490 032951 494160 114086 454022 260541 272925 744396 607999 413716 106504 240467 059982 544080 972119 944687 179409 371891 509715 > 4245 [i]