Best Known (111−80, 111, s)-Nets in Base 4
(111−80, 111, 34)-Net over F4 — Constructive and digital
Digital (31, 111, 34)-net over F4, using
- t-expansion [i] based on digital (21, 111, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 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) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(111−80, 111, 43)-Net in Base 4 — Constructive
(31, 111, 43)-net in base 4, using
- t-expansion [i] based on (30, 111, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
(111−80, 111, 60)-Net over F4 — Digital
Digital (31, 111, 60)-net over F4, using
- net from sequence [i] based on digital (31, 59)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 31 and N(F) ≥ 60, using
(111−80, 111, 133)-Net in Base 4 — Upper bound on s
There is no (31, 111, 134)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(4111, 134, S4, 80), but
- the linear programming bound shows that M ≥ 223116 977669 860225 490542 781243 340912 693123 115172 373758 967062 507381 385172 903920 664576 / 25797 158228 055065 > 4111 [i]