Best Known (122, 122+105, s)-Nets in Base 4
(122, 122+105, 130)-Net over F4 — Constructive and digital
Digital (122, 227, 130)-net over F4, using
- t-expansion [i] based on digital (105, 227, 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
(122, 122+105, 205)-Net over F4 — Digital
Digital (122, 227, 205)-net over F4, using
(122, 122+105, 2746)-Net in Base 4 — Upper bound on s
There is no (122, 227, 2747)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 226, 2747)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11795 220307 250636 987092 670694 954590 361846 018011 268288 430924 117973 022539 632175 436653 806054 456968 579149 885628 612008 793289 798122 495221 544310 > 4226 [i]