Best Known (122, 122+113, s)-Nets in Base 4
(122, 122+113, 130)-Net over F4 — Constructive and digital
Digital (122, 235, 130)-net over F4, using
- t-expansion [i] based on digital (105, 235, 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+113, 187)-Net over F4 — Digital
Digital (122, 235, 187)-net over F4, using
(122, 122+113, 2327)-Net in Base 4 — Upper bound on s
There is no (122, 235, 2328)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 234, 2328)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 779 952257 065672 993313 040318 116812 649620 498158 496836 603439 211380 933013 161884 146234 852976 489525 238899 146700 563822 160410 587064 861082 673728 320800 > 4234 [i]