Best Known (252−115, 252, s)-Nets in Base 4
(252−115, 252, 130)-Net over F4 — Constructive and digital
Digital (137, 252, 130)-net over F4, using
- t-expansion [i] based on digital (105, 252, 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
(252−115, 252, 235)-Net over F4 — Digital
Digital (137, 252, 235)-net over F4, using
(252−115, 252, 3249)-Net in Base 4 — Upper bound on s
There is no (137, 252, 3250)-net in base 4, because
- 1 times m-reduction [i] would yield (137, 251, 3250)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13 153426 326896 395605 436779 418305 269419 043840 601280 513328 514097 136268 795298 028903 869898 225143 998487 757657 414148 320734 424405 441879 444144 808484 016243 349616 > 4251 [i]