Best Known (12, 45, s)-Nets in Base 128
(12, 45, 288)-Net over F128 — Constructive and digital
Digital (12, 45, 288)-net over F128, using
- t-expansion [i] based on digital (9, 45, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(12, 45, 321)-Net over F128 — Digital
Digital (12, 45, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
(12, 45, 33378)-Net in Base 128 — Upper bound on s
There is no (12, 45, 33379)-net in base 128, because
- 1 times m-reduction [i] would yield (12, 44, 33379)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 521 675427 392764 867091 689657 762000 364024 551350 658241 018441 452392 570130 356686 803955 444963 891218 > 12844 [i]