MinT - Best Known (23, 50, s)-Nets in Base 4

Best Known (23, 50, s)-Nets in Base 4

(23, 50, 35)-Net over F₄ — Constructive and digital

Digital (23, 50, 35)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (3, 16, 14)-net over F₄, using
  - net from sequence [i] based on digital (3, 13)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]
2. digital (7, 34, 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]

(23, 50, 45)-Net over F₄ — Digital

Digital (23, 50, 45)-net over F₄, using

net from sequence [i] based on digital (23, 44)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 23 and N(F) ≥ 45, using
  - a curve from the manYPoints database [i]

(23, 50, 341)-Net in Base 4 — Upper bound on s

There is no (23, 50, 342)-net in base 4, because

1 times m-reduction [i] would yield (23, 49, 342)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 328719 355268 327597 637728 421670 > 4⁴⁹ [i]