Best Known (67, 135, s)-Nets in Base 4
(67, 135, 66)-Net over F4 — Constructive and digital
Digital (67, 135, 66)-net over F4, using
- t-expansion [i] based on digital (49, 135, 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
(67, 135, 100)-Net over F4 — Digital
Digital (67, 135, 100)-net over F4, using
(67, 135, 1081)-Net in Base 4 — Upper bound on s
There is no (67, 135, 1082)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1937 321231 807645 373254 096495 579693 372071 009435 758794 303474 146619 394526 133934 756604 > 4135 [i]