Best Known (107, 107+99, s)-Nets in Base 4
(107, 107+99, 130)-Net over F4 — Constructive and digital
Digital (107, 206, 130)-net over F4, using
- t-expansion [i] based on digital (105, 206, 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
(107, 107+99, 167)-Net over F4 — Digital
Digital (107, 206, 167)-net over F4, using
(107, 107+99, 2063)-Net in Base 4 — Upper bound on s
There is no (107, 206, 2064)-net in base 4, because
- 1 times m-reduction [i] would yield (107, 205, 2064)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2657 580856 383095 252876 718025 458077 623054 444653 044316 252388 752854 248983 118454 766430 921761 646758 578196 943333 672696 819576 762240 > 4205 [i]