Best Known (138−84, 138, s)-Nets in Base 4
(138−84, 138, 66)-Net over F4 — Constructive and digital
Digital (54, 138, 66)-net over F4, using
- t-expansion [i] based on digital (49, 138, 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
(138−84, 138, 91)-Net over F4 — Digital
Digital (54, 138, 91)-net over F4, using
- t-expansion [i] based on digital (50, 138, 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
(138−84, 138, 489)-Net in Base 4 — Upper bound on s
There is no (54, 138, 490)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 123431 275806 426296 403220 413419 970873 309305 381004 632192 449859 181770 001791 578102 494520 > 4138 [i]