Best Known (239−115, 239, s)-Nets in Base 4
(239−115, 239, 130)-Net over F4 — Constructive and digital
Digital (124, 239, 130)-net over F4, using
- t-expansion [i] based on digital (105, 239, 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
(239−115, 239, 190)-Net over F4 — Digital
Digital (124, 239, 190)-net over F4, using
(239−115, 239, 2356)-Net in Base 4 — Upper bound on s
There is no (124, 239, 2357)-net in base 4, because
- 1 times m-reduction [i] would yield (124, 238, 2357)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 198541 550999 590983 854221 007294 410623 581228 374829 419910 848421 506263 809402 049147 767867 600766 092725 692074 664105 790811 688926 782374 303640 143677 758720 > 4238 [i]