MinT - Best Known (30−22, 30, s)-Nets in Base 4

Best Known (30−22, 30, s)-Nets in Base 4

(30−22, 30, 21)-Net over F₄ — Constructive and digital

Digital (8, 30, 21)-net over F₄, using

t-expansion [i] based on digital (7, 30, 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]

(30−22, 30, 63)-Net in Base 4 — Upper bound on s

There is no (8, 30, 64)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 248582 399136 659529 > 4³⁰ [i]