MinT - Best Known (43, 43+76, s)-Nets in Base 3

Best Known (43, 43+76, s)-Nets in Base 3

(43, 43+76, 42)-Net over F₃ — Constructive and digital

Digital (43, 119, 42)-net over F₃, using

t-expansion [i] based on digital (39, 119, 42)-net over F₃, using
- net from sequence [i] based on digital (39, 41)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 39 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(43, 43+76, 56)-Net over F₃ — Digital

Digital (43, 119, 56)-net over F₃, using

t-expansion [i] based on digital (40, 119, 56)-net over F₃, using
- net from sequence [i] based on digital (40, 55)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
    - a curve from the manYPoints database [i]

(43, 43+76, 141)-Net in Base 3 — Upper bound on s

There is no (43, 119, 142)-net in base 3, because

1 times m-reduction [i] would yield (43, 118, 142)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹¹⁸, 142, S₃, 75), but
  - the linear programming bound shows that MÂ â‰¥ 364538 875344 058394 891301 059613 193584 850101 563950 604229 358063 537322 788761 / 1451 230757 361385 > 3¹¹⁸ [i]