Best Known (235−107, 235, s)-Nets in Base 4
(235−107, 235, 130)-Net over F4 — Constructive and digital
Digital (128, 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
(235−107, 235, 223)-Net over F4 — Digital
Digital (128, 235, 223)-net over F4, using
(235−107, 235, 3081)-Net in Base 4 — Upper bound on s
There is no (128, 235, 3082)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 234, 3082)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 770 473018 954786 551884 651179 008936 384834 851824 604032 840467 555433 198401 244327 172159 803128 924141 907547 377580 617596 181943 853020 076574 941747 790720 > 4234 [i]