MinT - Best Known (139−121, 139, s)-Nets in Base 3

Best Known (139−121, 139, s)-Nets in Base 3

(139−121, 139, 28)-Net over F₃ — Constructive and digital

Digital (18, 139, 28)-net over F₃, using

t-expansion [i] based on digital (15, 139, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(139−121, 139, 46)-Net in Base 3 — Upper bound on s

There is no (18, 139, 47)-net in base 3, because

3 times m-reduction [i] would yield (18, 136, 47)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹³⁶, 47, S₃, 3, 118), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 696198 609130 885597 695136 021593 547814 689632 716312 296141 651066 450089 / 7 > 3¹³⁶ [i]