MinT - Best Known (218−210, 218, s)-Nets in Base 4

Best Known (218−210, 218, s)-Nets in Base 4

(218−210, 218, 21)-Net over F₄ — Constructive and digital

Digital (8, 218, 21)-net over F₄, using

t-expansion [i] based on digital (7, 218, 21)-net over F₄, using
- net from sequence [i] based on digital (7, 20)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(218−210, 218, 34)-Net in Base 4 — Upper bound on s

There is no (8, 218, 35)-net in base 4, because

117 times m-reduction [i] would yield (8, 101, 35)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4¹⁰¹, 35, S₄, 3, 93), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 398 520634 976229 588334 406598 900608 325425 506342 458132 623154 741248 / 47 > 4¹⁰¹ [i]