MinT - Best Known (24, 24+40, s)-Nets in Base 3

Best Known (24, 24+40, s)-Nets in Base 3

(24, 24+40, 32)-Net over F₃ — Constructive and digital

Digital (24, 64, 32)-net over F₃, using

t-expansion [i] based on digital (21, 64, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(24, 24+40, 103)-Net in Base 3 — Upper bound on s

There is no (24, 64, 104)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁴, 104, S₃, 40), but
- the linear programming bound shows that MÂ â‰¥ 2 962004 263094 532507 337869 081743 858222 059094 257308 728871 435455 157099 / 842061 707484 948215 471641 634707 432925 > 3⁶⁴ [i]