MinT - Best Known (30−21, 30, s)-Nets in Base 4

Best Known (30−21, 30, s)-Nets in Base 4

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

Digital (9, 30, 22)-net over F₄, using

net from sequence [i] based on digital (9, 21)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
  - an explicitly constructive algebraic function field [i]

(30−21, 30, 26)-Net over F₄ — Digital

Digital (9, 30, 26)-net over F₄, using

net from sequence [i] based on digital (9, 25)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 26, using
  - Drinfeld modules of rank 1 [i]

(30−21, 30, 76)-Net in Base 4 — Upper bound on s

There is no (9, 30, 77)-net in base 4, because

1 times m-reduction [i] would yield (9, 29, 77)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 304143 562010 634226 > 4²⁹ [i]