Best Known (156−101, 156, s)-Nets in Base 4
(156−101, 156, 66)-Net over F4 — Constructive and digital
Digital (55, 156, 66)-net over F4, using
- t-expansion [i] based on digital (49, 156, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 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) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(156−101, 156, 91)-Net over F4 — Digital
Digital (55, 156, 91)-net over F4, using
- t-expansion [i] based on digital (50, 156, 91)-net over F4, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
(156−101, 156, 437)-Net in Base 4 — Upper bound on s
There is no (55, 156, 438)-net in base 4, because
- 1 times m-reduction [i] would yield (55, 155, 438)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2179 696618 910745 377034 214080 064741 505556 087419 903528 664705 740050 841717 178841 647006 398462 817298 > 4155 [i]