Best Known (134, 134+107, s)-Nets in Base 4
(134, 134+107, 130)-Net over F4 — Constructive and digital
Digital (134, 241, 130)-net over F4, using
- t-expansion [i] based on digital (105, 241, 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
(134, 134+107, 246)-Net over F4 — Digital
Digital (134, 241, 246)-net over F4, using
(134, 134+107, 3612)-Net in Base 4 — Upper bound on s
There is no (134, 241, 3613)-net in base 4, because
- 1 times m-reduction [i] would yield (134, 240, 3613)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3 153401 625313 522324 823787 084532 266067 902920 090875 270672 075367 281092 593984 312625 427154 952251 841709 083621 182476 518489 430440 889166 154122 708354 935360 > 4240 [i]