Best Known (124, 124+119, s)-Nets in Base 4
(124, 124+119, 130)-Net over F4 — Constructive and digital
Digital (124, 243, 130)-net over F4, using
- t-expansion [i] based on digital (105, 243, 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+119, 182)-Net over F4 — Digital
Digital (124, 243, 182)-net over F4, using
(124, 124+119, 2193)-Net in Base 4 — Upper bound on s
There is no (124, 243, 2194)-net in base 4, because
- 1 times m-reduction [i] would yield (124, 242, 2194)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 49 967649 195157 315294 343401 377654 880562 710974 558366 802008 828196 636482 819508 495122 321753 309021 985910 421798 113789 549100 593928 897442 204829 042046 617536 > 4242 [i]