MinT - Best Known (27−18, 27, s)-Nets in Base 4

Best Known (27−18, 27, s)-Nets in Base 4

(27−18, 27, 22)-Net over F₄ — Constructive and digital

Digital (9, 27, 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]

(27−18, 27, 26)-Net over F₄ — Digital

Digital (9, 27, 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]

(27−18, 27, 81)-Net in Base 4 — Upper bound on s

There is no (9, 27, 82)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 18603 346606 073218 > 4²⁷ [i]