Best Known (122, 122+99, s)-Nets in Base 4
(122, 122+99, 130)-Net over F4 — Constructive and digital
Digital (122, 221, 130)-net over F4, using
- t-expansion [i] based on digital (105, 221, 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+99, 222)-Net over F4 — Digital
Digital (122, 221, 222)-net over F4, using
(122, 122+99, 3175)-Net in Base 4 — Upper bound on s
There is no (122, 221, 3176)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 220, 3176)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2 846136 735194 973688 098655 955025 881277 078382 029485 590038 067992 426624 755315 016105 553592 278492 624716 558201 344376 269205 654466 114889 162380 > 4220 [i]