Best Known (36, 36+68, s)-Nets in Base 32
(36, 36+68, 120)-Net over F32 — Constructive and digital
Digital (36, 104, 120)-net over F32, using
- t-expansion [i] based on digital (11, 104, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
(36, 36+68, 216)-Net in Base 32 — Constructive
(36, 104, 216)-net in base 32, using
- 4 times m-reduction [i] based on (36, 108, 216)-net in base 32, using
- base change [i] based on (18, 90, 216)-net in base 64, using
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on (18, 90, 216)-net in base 64, using
(36, 36+68, 273)-Net over F32 — Digital
Digital (36, 104, 273)-net over F32, using
- t-expansion [i] based on digital (30, 104, 273)-net over F32, using
- net from sequence [i] based on digital (30, 272)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 30 and N(F) ≥ 273, using
- net from sequence [i] based on digital (30, 272)-sequence over F32, using
(36, 36+68, 281)-Net in Base 32
(36, 104, 281)-net in base 32, using
- 4 times m-reduction [i] based on (36, 108, 281)-net in base 32, using
- base change [i] based on digital (18, 90, 281)-net over F64, using
- net from sequence [i] based on digital (18, 280)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 18 and N(F) ≥ 281, using
- net from sequence [i] based on digital (18, 280)-sequence over F64, using
- base change [i] based on digital (18, 90, 281)-net over F64, using
(36, 36+68, 17525)-Net in Base 32 — Upper bound on s
There is no (36, 104, 17526)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3 436872 612393 571053 707338 341052 957932 790936 624011 952408 613532 238674 650688 222982 229900 902463 879295 785289 947398 777063 793311 903111 850707 566898 817454 602520 777426 > 32104 [i]