Best Known (132, 132+107, s)-Nets in Base 4
(132, 132+107, 130)-Net over F4 — Constructive and digital
Digital (132, 239, 130)-net over F4, using
- t-expansion [i] based on digital (105, 239, 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
(132, 132+107, 238)-Net over F4 — Digital
Digital (132, 239, 238)-net over F4, using
(132, 132+107, 3425)-Net in Base 4 — Upper bound on s
There is no (132, 239, 3426)-net in base 4, because
- 1 times m-reduction [i] would yield (132, 238, 3426)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 195149 672411 841182 724819 207053 086442 021267 514249 394974 060633 201102 809646 493309 361005 335415 088634 836077 292133 592528 015944 360495 462098 860319 362192 > 4238 [i]