Best Known (66, 66+141, s)-Nets in Base 4
(66, 66+141, 66)-Net over F4 — Constructive and digital
Digital (66, 207, 66)-net over F4, using
- t-expansion [i] based on digital (49, 207, 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
(66, 66+141, 99)-Net over F4 — Digital
Digital (66, 207, 99)-net over F4, using
- t-expansion [i] based on digital (61, 207, 99)-net over F4, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 61 and N(F) ≥ 99, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
(66, 66+141, 474)-Net in Base 4 — Upper bound on s
There is no (66, 207, 475)-net in base 4, because
- 1 times m-reduction [i] would yield (66, 206, 475)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11253 114151 736340 911031 915871 970435 422952 073011 089455 090215 947065 518536 025151 821297 576183 567968 358652 549778 754144 645749 729450 > 4206 [i]