Best Known (135, 135+111, s)-Nets in Base 4
(135, 135+111, 130)-Net over F4 — Constructive and digital
Digital (135, 246, 130)-net over F4, using
- t-expansion [i] based on digital (105, 246, 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
(135, 135+111, 239)-Net over F4 — Digital
Digital (135, 246, 239)-net over F4, using
(135, 135+111, 3374)-Net in Base 4 — Upper bound on s
There is no (135, 246, 3375)-net in base 4, because
- 1 times m-reduction [i] would yield (135, 245, 3375)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3237 118218 051836 464106 409909 581014 521314 707343 778770 655132 053629 890301 689077 655866 952148 281698 613669 940668 913765 759612 442652 286148 549647 370651 323456 > 4245 [i]