Best Known (124, 124+113, s)-Nets in Base 4
(124, 124+113, 130)-Net over F4 — Constructive and digital
Digital (124, 237, 130)-net over F4, using
- t-expansion [i] based on digital (105, 237, 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
(124, 124+113, 194)-Net over F4 — Digital
Digital (124, 237, 194)-net over F4, using
(124, 124+113, 2447)-Net in Base 4 — Upper bound on s
There is no (124, 237, 2448)-net in base 4, because
- 1 times m-reduction [i] would yield (124, 236, 2448)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12347 879628 722471 624300 498801 265917 829029 106629 474045 057618 421596 525811 720924 163012 975259 700381 748549 673859 972527 093940 979783 080585 872988 340600 > 4236 [i]