Best Known (135, 135+107, s)-Nets in Base 4
(135, 135+107, 130)-Net over F4 — Constructive and digital
Digital (135, 242, 130)-net over F4, using
- t-expansion [i] based on digital (105, 242, 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+107, 251)-Net over F4 — Digital
Digital (135, 242, 251)-net over F4, using
(135, 135+107, 3709)-Net in Base 4 — Upper bound on s
There is no (135, 242, 3710)-net in base 4, because
- 1 times m-reduction [i] would yield (135, 241, 3710)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12 631946 736700 773155 206999 715558 887754 586797 397629 155388 729886 500875 379251 887614 098448 149368 075929 772791 651987 828596 852569 741973 616486 432755 920865 > 4241 [i]