Best Known (249−125, 249, s)-Nets in Base 4
(249−125, 249, 130)-Net over F4 — Constructive and digital
Digital (124, 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
(249−125, 249, 173)-Net over F4 — Digital
Digital (124, 249, 173)-net over F4, using
(249−125, 249, 1991)-Net in Base 4 — Upper bound on s
There is no (124, 249, 1992)-net in base 4, because
- 1 times m-reduction [i] would yield (124, 248, 1992)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 207055 610162 891029 323353 217077 505142 073128 125066 180849 207106 740431 929853 528205 913837 639155 565530 839281 957516 308139 767657 447597 082456 400709 101809 534120 > 4248 [i]