Best Known (106, 106+82, s)-Nets in Base 4
(106, 106+82, 130)-Net over F4 — Constructive and digital
Digital (106, 188, 130)-net over F4, using
- t-expansion [i] based on digital (105, 188, 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
(106, 106+82, 210)-Net over F4 — Digital
Digital (106, 188, 210)-net over F4, using
(106, 106+82, 3067)-Net in Base 4 — Upper bound on s
There is no (106, 188, 3068)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 155647 825433 383294 626183 865487 952881 344280 324883 034469 922762 323816 478039 268360 363538 896881 468867 473511 826311 049075 > 4188 [i]