Best Known (59, 59+104, s)-Nets in Base 4
(59, 59+104, 66)-Net over F4 — Constructive and digital
Digital (59, 163, 66)-net over F4, using
- t-expansion [i] based on digital (49, 163, 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
(59, 59+104, 91)-Net over F4 — Digital
Digital (59, 163, 91)-net over F4, using
- t-expansion [i] based on digital (50, 163, 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
(59, 59+104, 478)-Net in Base 4 — Upper bound on s
There is no (59, 163, 479)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 144 313724 663995 581660 253385 895752 484880 640068 943079 687904 972357 544092 305023 435617 720001 735362 199290 > 4163 [i]